Math

QuestionSolve the inequality 2(4z+5)>2z22-2(4 z+5)>-2 z-22 and graph the solution.

Studdy Solution

STEP 1

Assumptions1. The inequality to solve is (4z+5)>z22-(4 z+5)>- z-22 . We need to find the values of zz that satisfy this inequality3. We will then graph the solution on a number line

STEP 2

First, we need to simplify the inequality. We can do this by distributing the 2-2 on the left side of the inequality.
2(4z+5)=8z10-2(4 z+5) = -8z -10So, the inequality becomes8z10>2z22-8z -10 > -2z -22

STEP 3

Next, we need to isolate zz on one side of the inequality. We can do this by adding 8z8z to both sides of the inequality.
10>6z22-10 >6z -22

STEP 4

Now, add 2222 to both sides of the inequality to isolate 6z6z on one side.
12>6z12 >6z

STEP 5

Finally, divide both sides of the inequality by $$ to solve for $z$.
z<2z <2

STEP 6

Now that we have the solution to the inequality, we can graph it on a number line. The solution z<2z <2 means that zz can be any number less than 22.
To graph this, draw a number line and mark the point 22. Since zz is less than 22, we will draw an open circle at 22 and shade the line to the left of 22.

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