Ask a New Question
Menu

Solve x - 2.41 > 4.76

x < 7.17
x < 2.35
x > 7.17
x > 2.35

11 answers

To solve the inequality \( x - 2.41 > 4.76 \), we can isolate \( x \) by adding \( 2.41 \) to both sides of the inequality:

\[ x > 4.76 + 2.41 \]

Calculating the right side:

\[ x > 7.17 \]

So, the solution to the inequality \( x - 2.41 > 4.76 \) is \( x > 7.17 \).

Now, let's look at the other inequalities given:

  1. \( x < 7.17 \)
  2. \( x < 2.35 \)
  3. \( x > 7.17 \)
  4. \( x > 2.35 \)

Based on the inequality we solved, the correct answer is \( x > 7.17 \). Thus, among the options provided, the correct solution is:

  • \( x > 7.17 \)
Josie solved an inequality and graphed the solution on the number line. Which or the following inequalities did she solve?
it has a closed circle on 2.50 and an arrow pointing to the right
x - 1.25 ≥ 1.25
x - 1.25 ≤ 1.25
x + 1.25 ≥ 1.25
x + 0.5 < 3

To determine which inequality corresponds to a closed circle on \(2.50\) with an arrow pointing to the right, we can analyze the given inequalities one by one.

  1. Inequality: \(x - 1.25 \geq 1.25\)

    \[ x - 1.25 \geq 1.25 \]

    Add \(1.25\) to both sides:

    \[ x \geq 2.5 \]

    This represents a closed circle at \(2.50\) with an arrow pointing to the right.

  2. Inequality: \(x - 1.25 \leq 1.25\)

    \[ x - 1.25 \leq 1.25 \]

    Add \(1.25\) to both sides:

    \[ x \leq 2.5 \]

    This represents a closed circle at \(2.50\) with an arrow pointing to the left.

  3. Inequality: \(x + 1.25 \geq 1.25\)

    \[ x + 1.25 \geq 1.25 \]

    Subtract \(1.25\) from both sides:

    \[ x \geq 0 \]

    This would represent a closed circle at \(0\) with an arrow pointing to the right.

  4. Inequality: \(x + 0.5 < 3\)

    \[ x + 0.5 < 3 \]

    Subtract \(0.5\) from both sides:

    \[ x < 2.5 \]

    This represents an open circle at \(2.50\) with an arrow pointing to the left.

Conclusion:

The inequality that corresponds to a closed circle at \(2.50\) with an arrow pointing to the right is:

\(x - 1.25 \geq 1.25\).

Solve 1.7x ≥ 5.95
x ≥ 10.115
x ≥ 7.65
x ≥ 4.25
x ≥ 3.5

To solve the inequality \(1.7x \geq 5.95\), we need to isolate \(x\).

Here's how to do it step-by-step:

  1. Divide both sides by 1.7 (make sure to keep the direction of the inequality the same because we are dividing by a positive number):

\[ x \geq \frac{5.95}{1.7} \]

  1. Perform the calculation on the right side:

\[ \frac{5.95}{1.7} \approx 3.5 \]

So, the solution is:

\[ x \geq 3.5 \]

Now, let's look at the options you provided:

  • \(x \geq 10.115\)
  • \(x \geq 7.65\)
  • \(x \geq 4.25\)
  • \(x \geq 3.5\)

The correct answer is:

\(x \geq 3.5\).

Solve -5x + 12 < 32
x < 4
x > -4
x > 4
x < -4

To solve the inequality \(-5x + 12 < 32\), we can follow these steps:

  1. Subtract 12 from both sides:

    \[ -5x < 32 - 12 \]

    \[ -5x < 20 \]

  2. Divide both sides by -5: (When dividing by a negative number, remember to reverse the inequality sign.)

    \[ x > \frac{20}{-5} \]

    \[ x > -4 \]

So, the solution to the inequality \(-5x + 12 < 32\) is:

\(x > -4\).

Now, let's look at the options you provided:

  • \(x < 4\)
  • \(x > -4\)
  • \(x > 4\)
  • \(x < -4\)

The correct answer is:

\(x > -4\).

Eric is solving the inequality 9x + 15 ≥ 51 and graphing the solution. Which of the following describe the steps he should take using inverse operations to solve?
Subtract 15 from both sides of the inequality and then divide both sides of the inequality by 9.
Divide both sides of the inequality by 9 and then subtract 15 from both sides of the inequality.
Divide both sides of the inequality by 9 and then add 15 to both sides of the inequality.
Subtract 15 from both sides of the inequality and then multiply both sides of the inequality by 9.

To solve the inequality \(9x + 15 \geq 51\) using inverse operations, we need to first eliminate the constant term on the left side (which is \(15\)), and then isolate \(x\) by dealing with the coefficient in front of \(x\) (which is \(9\)).

Let's break it down step-by-step:

  1. Start with the inequality: \[ 9x + 15 \geq 51 \]

  2. Subtract 15 from both sides: \[ 9x \geq 51 - 15 \] \[ 9x \geq 36 \]

  3. Divide both sides by 9: \[ x \geq \frac{36}{9} \] \[ x \geq 4 \]

Conclusion:

The correct steps that Eric should take to solve the inequality are:

Subtract 15 from both sides of the inequality and then divide both sides of the inequality by 9.

This matches the first option you provided.

Help Eric draw his answer on the number line by selecting the correct responses below.
Eric would plot the point given in the solution on the number line with a(n) ____ circle and shade to the _____ of the point on the number line.

Since Eric's solution to the inequality \(9x + 15 \geq 51\) is \(x \geq 4\), here's how he would represent this on the number line:

  1. Plot the point: Since the inequality is "greater than or equal to" (\(\geq\)), Eric would plot the point corresponding to \(4\).

  2. Circle type: Because it includes the equal sign, he would use a closed circle at \(4\). This indicates that \(4\) is included in the solution set.

  3. Direction to shade: The inequality \(x \geq 4\) means that \(x\) can take on any value greater than \(4\). Therefore, he would shade to the right of the point \(4\) on the number line.

Final Statement:

Eric would plot the point given in the solution on the number line with a(n) closed circle and shade to the right of the point on the number line.