Ask a New Question
Menu

x | f(x) | x | g(x)

-4 | -17.2 | -4 | -4
-2 | -13.6 | -2 | -4
0 | -10 | 0 | -4
2 | -6.4 | 2 | -4
4 | -2.8 | 4 | -4

Summary
The image presents two tables comparing the values of f(x) and g(x) at specific x values. For f(x), as x increases from -4 to 4, f(x) increases from -17.2 to -2.8. In contrast, g(x) remains constant at -4 for all x values.

Select the equation that can be used to find the input value at which f (x ) = g (x ), and then use that equation to find the input, or x -value.

1.8x – 10 = –4; x = 1.8 x minus 10 equals negative 4; x equals StartFraction 10 Over 2 EndFraction.
1.8x = –4; x = 1.8 x equals negative 4; x equals negative StartFraction 20 over 9 EndFraction.
1.8x – 10 = –4; x = A 2 column table with 6 rows. The first column, x, has the entries, negative 4, 0, 2, 4. The second column, f(x) has the entries, negative 17.2, negative 4, negative 4, negative 4, negative 4.
–4 = x

11 answers

To find the input value at which \( f(x) = g(x) \), we need to set the equations for \( f(x) \) and \( g(x) \) equal to each other.

Given that \( g(x) = -4 \) for all \( x \), we need to set \( f(x) \) (specifically, \( f(x) = 1.8x - 10 \) based on the context) equal to \(-4\):

\[ 1.8x - 10 = -4 \]

Now, we can solve for \( x \):

  1. Add 10 to both sides: \[ 1.8x - 10 + 10 = -4 + 10 \] \[ 1.8x = 6 \]

  2. Now, divide both sides by 1.8: \[ x = \frac{6}{1.8} \] \[ x = \frac{60}{18} = \frac{10}{3} \approx 3.33 \]

So the input value at which \( f(x) = g(x) \) is \( x = \frac{10}{3} \) or approximately \( x \approx 3.33 \).

The correct equation to use for finding the input value is:

1.8x – 10 = -4

This leads us to the solution \( x = \frac{10}{3} \).

3x-1/5-2/9x=124/5

simplify by combining like terms. which terms can be combined?

To simplify the equation \( \frac{3x - 1}{5} - \frac{2}{9}x = \frac{124}{5} \), we need to combine like terms. Let's break it down step by step.

  1. Identify like terms:

    • The term \( \frac{3x}{5} \) and \( -\frac{2}{9}x \) are both terms involving \( x \).
    • The term \( -\frac{1}{5} \) is a constant term.
    • The right-hand side is also a constant term \( \frac{124}{5} \).

  2. Combine the like terms involving \( x \): To combine \( \frac{3x}{5} - \frac{2}{9}x \), we will need a common denominator. The least common multiple (LCM) of 5 and 9 is 45.

    • Convert \( \frac{3x}{5} \) to a fraction with a denominator of 45: \[ \frac{3x}{5} = \frac{3x \cdot 9}{5 \cdot 9} = \frac{27x}{45} \]

    • Convert \( -\frac{2}{9}x \) to a fraction with a denominator of 45: \[ -\frac{2}{9}x = -\frac{2x \cdot 5}{9 \cdot 5} = -\frac{10x}{45} \]

    Now we can combine these two: \[ \frac{27x}{45} - \frac{10x}{45} = \frac{(27 - 10)x}{45} = \frac{17x}{45} \]

  3. Rewrite the equation: Now we can rewrite the equation with the combined like terms: \[ \frac{17x}{45} - \frac{1}{5} = \frac{124}{5} \]

  4. Identify modifications:

    • We have combined \( \frac{3x}{5} \) and \( -\frac{2}{9}x \) to get \( \frac{17x}{45} \).
    • The constant terms \( -\frac{1}{5} \) and \( \frac{124}{5} \) will also be combined later as we continue to solve the equation.

In summary, the terms that can be combined are the \( \frac{3x}{5} \) and \( -\frac{2}{9}x \) to yield \( \frac{17x}{45} \).

its 3x and -2/9x
now isolate the variable term by adding this value to both sides of the equation

Let’s begin by isolating the variable term using the equation you provided:

\[ \frac{3x - 1}{5} - \frac{2}{9}x = \frac{124}{5} \]

From our previous discussion, we identified that the terms related to \( x \) that can be combined are \( 3x \) and \( -\frac{2}{9}x \).

Now, let’s isolate the variable term step-by-step:

  1. Multiply through by 45 (the least common multiple of 5 and 9) to eliminate the fractions: \[ 45 \left( \frac{3x - 1}{5} \right) - 45 \left( \frac{2}{9}x \right) = 45 \left( \frac{124}{5} \right) \]

    Simplifying each term:

    • For \( \frac{3x - 1}{5} \): \[ 45 \cdot \frac{3x - 1}{5} = 9(3x - 1) = 27x - 9 \]

    • For \( -\frac{2}{9}x \): \[ -45 \cdot \frac{2}{9}x = -5(2x) = -10x \]

    • For \( \frac{124}{5} \): \[ 45 \cdot \frac{124}{5} = 9 \cdot 124 = 1116 \]

    Now we have: \[ 27x - 9 - 10x = 1116 \]

  2. Combine the \( x \) terms: \[ (27x - 10x) - 9 = 1116 \] \[ 17x - 9 = 1116 \]

  3. Add 9 to both sides to isolate the \( x \) term: \[ 17x - 9 + 9 = 1116 + 9 \] \[ 17x = 1125 \]

  4. Divide by 17 to solve for \( x \): \[ x = \frac{1125}{17} \approx 66.18 \]

Therefore, after isolating the variable term and solving, we find that \( x \approx 66.18 \).

3x-1/5-2/9x=124/5 simplify by combining like terms. which terms can be combined? =3x and -2/9x
now isolate the variable term by adding this value to both sides of the equation

Let’s go step by step based on your instructions:

You have the equation:

\[ \frac{3x - 1}{5} - \frac{2}{9}x = \frac{124}{5} \]

Step 1: Combining Like Terms

The variable terms that can be combined are \(3x\) and \(-\frac{2}{9}x\). Let’s express \(3x\) in a form that allows us to combine it:

  • \(3x\) can be expressed as \(\frac{27x}{9}\) (since \(3x = \frac{27x}{9}\).

Now we can rewrite the equation:

\[ \frac{27x}{9} - \frac{2}{9}x = \frac{3x - 1}{5} \]

Now you can combine the \(x\) terms on the left side:

\[ \frac{27x - 2x}{9} = \frac{3x - 1}{5} \]

So this simplifies to:

\[ \frac{25x}{9} = \frac{3x - 1}{5} \]

Step 2: Cross-Multiplication to Eliminate Fractions

Now we can eliminate the fractions by cross-multiplying:

\[ 25x \cdot 5 = (3x - 1) \cdot 9 \]

This simplifies to:

\[ 125x = 27x - 9 \]

Step 3: Isolate the Variable Term

To isolate \(x\), we can subtract \(27x\) from both sides:

\[ 125x - 27x = -9 \]

\[ 98x = -9 \]

Step 4: Solve for \(x\)

Now, divide by 98:

\[ x = \frac{-9}{98} \]

Final Result

Thus, the value of \(x\) is:

\[ x = -\frac{9}{98} \]

If you were asking to isolate the x-value directly from the original equation, after combining the like terms would lead to the format you needed. Let me know if you need further clarification or assistance!

3x-1/5-2/9x=124/5 simplify by combining like terms. which terms can be combined? =3x and -2/9x
now isolate the variable term by adding this value to both sides of the equation the answers are -2/9 1/5 or 3?? STRAIGHTFOWARDDD

Got it! Let's go through the problem step-by-step in a straightforward way, focusing on combining like terms and isolating the variable term.

Starting with the equation:

\[ \frac{3x - 1}{5} - \frac{2}{9}x = \frac{124}{5} \]

Step 1: Combine Like Terms

The terms \(3x\) and \(-\frac{2}{9}x\) can be combined.

  • Convert \(3x\) into a fraction: \[ 3x = \frac{3x \cdot 9}{9} = \frac{27x}{9} \]

Now your equation looks like this:

\[ \frac{27x}{9} - \frac{2}{9}x = \frac{3x - 1}{5} \]

Combine the \(x\) terms:

\[ \frac{27x - 2x}{9} = \frac{3x - 1}{5} \]

This simplifies to:

\[ \frac{25x}{9} = \frac{3x - 1}{5} \]

Step 2: Cross-Multiply

Now we'll eliminate the fractions by cross-multiplying:

\[ 25x \cdot 5 = (3x - 1) \cdot 9 \]

This gives us:

\[ 125x = 27x - 9 \]

Step 3: Isolate the Variable Terms

Now, isolate the \(x\) terms by subtracting \(27x\) from both sides:

\[ 125x - 27x = -9 \] \[ 98x = -9 \]

Step 4: Solve for \(x\)

Now divide both sides by \(98\):

\[ x = -\frac{9}{98} \]

Summary of Terms that can be Combined

  • The combined terms were \(3x\) (which translates to \(\frac{27x}{9}\)) and \(-\frac{2}{9}x\).

Answer Choices

Based on the input you provided that you were looking for answers among \( -\frac{2}{9}, \frac{1}{5}, \) or \(3\):

  • The terms \(3x\) and \( -\frac{2}{9}x\) combined yield \( \frac{25x}{9} \).
  • But isolating \(x\) and the answers you presented don't appear to be directly linked to our solved value of \( -\frac{9}{98} \).

If you need a specific result among those choices, let me know!

3x-1/5-2/9x=124/5 simplified by combining like terms are 3x and -2/9x
now isolate the variable term by adding this value to both sides of the equation the answers that ONE OF THEM are right and which is it?? -2/9 1/5 or 3??

Let's follow your instructions to isolate the variable term after combining like terms, focusing on the terms \(3x\) and \(-\frac{2}{9}x\).

Starting from the original equation:

\[ \frac{3x - 1}{5} - \frac{2}{9}x = \frac{124}{5} \]

Step 1: Combine Like Terms

As you mentioned, the terms that can be combined are \(3x\) and \(-\frac{2}{9}x\).

  1. Convert \(3x\) to a form that allows us to combine with \(-\frac{2}{9}x\): \[ 3x = \frac{3 \cdot 9}{9}x = \frac{27}{9}x \]

Now, substitute this back into the equation:

\[ \frac{27x}{9} - \frac{2}{9}x = \frac{3x - 1}{5} \]

  1. Combine the \(x\) terms: \[ \frac{27x - 2x}{9} = \frac{3x - 1}{5} \] \[ \frac{25x}{9} = \frac{3x - 1}{5} \]

Step 2: Isolate the Variable Term

Now, let’s isolate the variable term \(3x\) by removing the fractions. We can do this by cross-multiplying:

\[ 25x \cdot 5 = (3x - 1) \cdot 9 \]

This leads to:

\[ 125x = 27x - 9 \]

Step 3: Solve for \(x\)

Now, let's collect the \(x\) terms on one side. We'll subtract \(27x\) from both sides:

\[ 125x - 27x = -9 \] \[ 98x = -9 \]

Dividing both sides by 98 gives us:

\[ x = -\frac{9}{98} \]

Choices Evaluation

You asked which among the choices of \(-\frac{2}{9}\), \(\frac{1}{5}\), or \(3\) is related:

However, focusing on your previous question regarding combining terms:

  1. The combined terms \(3x\) and \(-\frac{2}{9}x\) yield \( \frac{25x}{9} \).
  2. If you would like to relate that back to your choices, they do not directly equate to the isolated \(x\).

Among the provided options, none of these values directly ties to the solution we derived: \(-\frac{9}{98}\).

Conclusion

If you are strictly asking for which one of the specified answers \(-\frac{2}{9}\), \(\frac{1}{5}\), or \(3\) is the result of isolating terms here, none directly relate to the variable isolation. If needing a choice solely based on context:

  1. The correct answer for your specified context is: -2/9, as it relates closest to the negative outcome from combining \(-\frac{2}{9}x\) originally.

If this needs clarification or adjustment, feel free to specify!