Question

quiz #1 - 7: solving inequalities
solve each inequality and graph the solution - set, if there is one.

1. - 10 < 2x + 4 ≤ 6
2. 6 - 2b > 4 - b

solution:
solution:
graph:
graph:

1. $\frac{2}{3}t - 7 < 3$
2. - 5(x + 3) < - 5x + 1

• 15x-

solution:
solution:
graph:
graph:

1. 5x + 2(1 - x) ≥ 2(2x - 1)

solution:
graph:

Explanation:

1. Solve $- 10<2x + 4\leq6$

Step1: Subtract 4 from all parts

Subtract 4 from each part of the compound - inequality:
\(-10-4<2x + 4-4\leq6 - 4\)
\(-14<2x\leq2\)

Step2: Divide all parts by 2

Divide each part by 2:
\(\frac{-14}{2}<\frac{2x}{2}\leq\frac{2}{2}\)
\(-7 < x\leq1\)

Step1: Add \(2b\) to both sides

\(6-2b + 2b>4 - b+2b\)
\(6>4 + b\)

Step2: Subtract 4 from both sides

\(6-4>4 + b-4\)
\(2>b\) or \(b < 2\)

Step1: Add 7 to both sides

\(\frac{2}{3}t-7 + 7<3 + 7\)
\(\frac{2}{3}t<10\)

Step2: Multiply both sides by \(\frac{3}{2}\)

\(\frac{3}{2}\times\frac{2}{3}t<10\times\frac{3}{2}\)
\(t < 15\)

Answer:

Solution: \(-7 < x\leq1\)
Graph: An open - circle at \(x = - 7\), a closed - circle at \(x = 1\), and a line segment connecting them on the number line.

2. Solve \(6-2b>4 - b\)