Question

linear inequalities with decimals
question
solve the following inequality:
7 < 6.4 + 3(-6x - 4.3)
answer
attempt 1 out of 2

Explanation:

Step1: Distribute the 3

First, we distribute the 3 into the parentheses: \( 3(-6x - 4.3) = -18x - 12.9 \). So the inequality becomes \( 7 < 6.4 - 18x - 12.9 \).

Step2: Combine like terms

Next, we combine the constant terms on the right side: \( 6.4 - 12.9 = -6.5 \). Now the inequality is \( 7 < -18x - 6.5 \).

Step3: Add 6.5 to both sides

We add 6.5 to both sides to isolate the term with \( x \): \( 7 + 6.5 < -18x \), which simplifies to \( 13.5 < -18x \).

Step4: Divide both sides by -18 (and reverse the inequality)

When we divide both sides by a negative number, we reverse the inequality sign. So \( \frac{13.5}{-18} > x \), which simplifies to \( -0.75 > x \) or \( x < -0.75 \).

Answer:

\( x < -0.75 \)