Math Problem Statement

Which inequality is equivalent to the given inequality? -4(x + 7) < 3(x - 2)

Solution

The inequality provided is:

4(x+7)<3(x2)-4(x + 7) < 3(x - 2)

Let's solve this step-by-step to find the equivalent inequality.

Step 1: Expand both sides.

  • Left side: 4(x+7)=4x28-4(x + 7) = -4x - 28
  • Right side: 3(x2)=3x63(x - 2) = 3x - 6

Thus, the inequality becomes: 4x28<3x6-4x - 28 < 3x - 6

Step 2: Combine like terms.

  • Add 4x4x to both sides: 28<7x6-28 < 7x - 6

  • Add 66 to both sides: 28+6<7x-28 + 6 < 7x 22<7x-22 < 7x

Step 3: Solve for xx.

  • Divide both sides by 77: x>227x > -\frac{22}{7}

Thus, the inequality is x>227x > -\frac{22}{7}, but we are looking for an inequality that matches the format in the options.

Step 4: Compare to the options provided.

We need to match the inequality with one of the options. From the options, we see they are looking at the equivalent form in terms of 7x-7x.

The inequality becomes: 7x>22-7x > 22

So, the correct answer is Option D: 7x>22-7x > 22.

Would you like further details or have any other questions?

Here are 5 related questions to expand on this topic:

  1. How do you solve inequalities with negative coefficients?
  2. What is the effect of multiplying or dividing an inequality by a negative number?
  3. How do you graph the solution of an inequality on a number line?
  4. Can you provide a real-world example where inequalities are used?
  5. What are the key differences between solving an inequality and solving an equation?

Tip: When solving inequalities, remember to flip the inequality sign when multiplying or dividing by a negative number.

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Linear Equations

Formulas

Distributive Property
Combining Like Terms

Theorems

Properties of Inequalities

Suitable Grade Level

Grades 8-10