Question

answer the following given the inequality 4x - 4 < 24. a. what is the first step for solving this inequality? b. what is the solution to this inequality? c. what is the graph of the solution?

Explanation:

Step1: Isolate the variable term

Add 4 to both sides of the inequality $4x - 4<24$. So we get $4x-4 + 4<24 + 4$, which simplifies to $4x<28$.

Step2: Solve for x

Divide both sides of the inequality $4x<28$ by 4. We have $\frac{4x}{4}<\frac{28}{4}$, so $x < 7$.

Step3: Find the first - step answer

The first step for solving $4x - 4<24$ is adding 4 to both sides.

Step4: Find the solution

The solution of the inequality $4x - 4<24$ is $x < 7$.

Step5: Graph the solution

On a number line, draw an open circle at 7 (because 7 is not included in the solution $x < 7$) and shade the line to the left of 7.

Answer:

a. The first step for solving this inequality is adding 4 to both sides.
b. The solution to this inequality is $x < 7$.
c. The graph of the solution: An open - circle at 7 and shading to the left on the number line.