Question

pcm
mid - unit 2 quiz

1. solve for x. show work.

5 - 2(x + 3)=9

1. evaluate the expression if x = - 5,y = 2

7y

+

x + 1

1. solve the inequality. then graph the solution.

7 - 2x>11

Explanation:

Step1: Solve \(5 - 2(x + 3)=9\)

First, expand the left - hand side using the distributive property \(a(b + c)=ab+ac\). So, \(5-2x-6 = 9\). Then simplify the left - hand side: \(-2x - 1=9\). Add \(1\) to both sides: \(-2x=9 + 1\), which gives \(-2x=10\). Divide both sides by \(-2\): \(x=\frac{10}{-2}=-5\).

Step2: Evaluate \(|7y|+|x + 1|\) when \(x=-5,y = 2\)

Substitute \(x=-5\) and \(y = 2\) into the expression. First, find \(|7y|\): since \(y = 2\), \(|7y|=|7\times2|=|14| = 14\). Second, find \(|x + 1|\): substitute \(x=-5\), then \(|x + 1|=|-5 + 1|=|-4|=4\). Add the two results: \(14+4=18\).

Step3: Solve \(7-2x>11\)

Subtract \(7\) from both sides: \(-2x>11 - 7\), so \(-2x>4\). Divide both sides by \(-2\). When dividing an inequality by a negative number, the inequality sign flips. So \(x<-2\). To graph \(x < - 2\), draw an open circle at \(-2\) on the number line and shade to the left.

Answer:

1. \(x=-5\)
2. \(18\)
3. \(x < - 2\) (graph: open circle at \(-2\), shade left)