Question

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

a
4 5 6 7 8 9 10

b
2 3 4 5 6 7 8

c
4 5 6 7 8 9 10

d
2 3 4 5 6 7 8
a
add 4 to both sides
subtract 4 from both sides
multiply 4 to both sides
divide 4 from both sides
b
x < 5
x > 5
x < 7
x > 7

Explanation:

Step1: Isolate the variable - term

To solve the inequality $4x - 4<16$ (assuming the right - hand side is 16 as it's cut off), the first step is to get rid of the constant term on the left - hand side. We do this by adding 4 to both sides of the inequality. The general rule for solving inequalities like $ax + b < c$ is to first use the addition or subtraction property of inequalities to isolate the term with the variable.
$4x-4 + 4<16 + 4$

Step2: Simplify and solve for x

After adding 4 to both sides, we get $4x<20$. Then, using the division property of inequalities (divide both sides by 4 since 4 is positive and the direction of the inequality sign remains the same), we have $x < 5$.
$\frac{4x}{4}<\frac{20}{4}$

Answer:

a. Add 4 to both sides
b. $x < 5$
c. The graph of $x < 5$ is a number line with an open circle at 5 (because 5 is not included in the solution set) and an arrow pointing to the left. So the correct graph is the one with an open - circle at 5 and the line going to the left, which is option D in the given graph choices.