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help me how to solve this 3/4x+3-2x=-1/4+1/2x+5

ive already combined terms

9 answers

Let's solve the equation step by step. The original equation is:

\[ \frac{3}{4}x + 3 - 2x = -\frac{1}{4} + \frac{1}{2}x + 5 \]

You mentioned that you've already combined terms, so let's start by simplifying both sides.

Step 1: Simplify Both Sides

First, simplify the left side:

\[ \frac{3}{4}x - 2x + 3 \]

To combine \(\frac{3}{4}x\) and \(-2x\), convert \(-2x\) into a fraction with a denominator of 4:

\[ -2x = -\frac{8}{4}x \]

Now combine them:

\[ \frac{3}{4}x - \frac{8}{4}x + 3 = -\frac{5}{4}x + 3 \]

So, the left side simplifies to:

\[ -\frac{5}{4}x + 3 \]

Now, simplify the right side:

\[ -\frac{1}{4} + \frac{1}{2}x + 5 \]

Transform \(5\) into a fraction:

\[ 5 = \frac{20}{4} \]

Combine the constants:

\[ -\frac{1}{4} + \frac{20}{4} = \frac{19}{4} \]

So, the right side simplifies to:

\[ \frac{1}{2}x + \frac{19}{4} \]

Step 2: Combine the simplified expressions

Now we can rewrite the equation as:

\[ -\frac{5}{4}x + 3 = \frac{1}{2}x + \frac{19}{4} \]

Step 3: Clear the fractions

To eliminate the fractions, we can multiply the entire equation by 4 (the common denominator):

\[ 4 \left(-\frac{5}{4}x\right) + 4(3) = 4\left(\frac{1}{2}x\right) + 4\left(\frac{19}{4}\right) \]

This gives:

\[ -5x + 12 = 2x + 19 \]

Step 4: Move all terms involving \(x\) to one side and constants to the other side

\[ -5x - 2x = 19 - 12 \]

Simplifying gives:

\[ -7x = 7 \]

Step 5: Solve for \(x\)

Divide both sides by -7:

\[ x = -1 \]

Final Answer

Thus, the solution to the equation is:

\[ x = -1 \]

one by one please

Sure! Let's go through the solution step by step.

Step 1: Write the original equation

The original equation is: \[ \frac{3}{4}x + 3 - 2x = -\frac{1}{4} + \frac{1}{2}x + 5 \]

Step 2: Combine like terms on both sides

Let's start with the left side \( \frac{3}{4}x + 3 - 2x\).

  • First, we need to combine \(\frac{3}{4}x\) and \(-2x\). We can rewrite \(-2x\) with a common denominator of 4: \[ -2x = -\frac{8}{4}x \] Now, combine: \[ \frac{3}{4}x - \frac{8}{4}x = -\frac{5}{4}x \]

Thus, the left side simplifies to: \[ -\frac{5}{4}x + 3 \]

Now for the right side: \(-\frac{1}{4} + \frac{1}{2}x + 5\). Change \(5\) into a fraction with a denominator of 4: \[ 5 = \frac{20}{4} \] Now combine the constants: \[ -\frac{1}{4} + \frac{20}{4} = \frac{19}{4} \] So, the right side simplifies to: \[ \frac{1}{2}x + \frac{19}{4} \]

Step 3: Rewrite the equation

With both sides simplified, the equation now looks like: \[ -\frac{5}{4}x + 3 = \frac{1}{2}x + \frac{19}{4} \]

Would you like to proceed to the next step?

hey no like LITTERALLY one at a time not all together like

1st combine terms

then i ask whats next??

you add 3

LIKE THAT

Got it! Let's go step by step, one action at a time.

Step 1: Combine like terms on the left side of the equation.

Start with the original equation: \[ \frac{3}{4}x + 3 - 2x = -\frac{1}{4} + \frac{1}{2}x + 5 \]

Now, combine the terms on the left side: \(\frac{3}{4}x\) and \(-2x\).

What do you want to do next?

tell me the next step

Step 2: Combine \(\frac{3}{4}x\) and \(-2x\).

To combine these, we need to rewrite \(-2x\) as a fraction with a denominator of 4:

\[ -2x = -\frac{8}{4}x \]

Now combine \(\frac{3}{4}x\) and \(-\frac{8}{4}x\):

\[ \frac{3}{4}x - \frac{8}{4}x = -\frac{5}{4}x \]

So the left side becomes: \[ -\frac{5}{4}x + 3 \]

Would you like to proceed to the next step?

3/4x+3-2x=-1/4+1/2x+5
combine terms
-5/4x+3=19/4+1/2x
subtract 1/2
-7/4x+3=19/4
subtract 3
-7/4x=7/4
multiply -4/7
x=-1

SEE WHAT I DID THERE??

I WANTED YOU YOUUUUU TO DO THAT

Got it! Sorry for the misunderstanding. Let's follow your approach step by step.

Start with the original equation:

\[ \frac{3}{4}x + 3 - 2x = -\frac{1}{4} + \frac{1}{2}x + 5 \]

Step 1: Combine Terms

Let's do that:

On the left side: \[ -\frac{5}{4}x + 3 \]

On the right side: \[ \frac{19}{4} + \frac{1}{2}x \]

So we get: \[ -\frac{5}{4}x + 3 = \frac{19}{4} + \frac{1}{2}x \]

Step 2: Now, subtract \(\frac{1}{2}x\) from both sides

What do you want to do next?