QuestionSolve the inequality $0 \leq 2z + 5 < 8$ .

Studdy Solution

STEP 1

Assumptions1. The inequality is $0 \leq z+5<8$ . We are solving for $z$

STEP 2

The inequality is a compound inequality, meaning it has two parts. We will solve each part separately. The first part is $0 \leq2 z+5$ .

STEP 3

To isolate $z$ in the first part of the inequality, we need to subtract5 from both sides.
$0 -5 \leq2 z +5 -5$

STEP 4

implify the inequality.
$- \leq2z$

STEP 5

Next, divide both sides by2 to solve for $z$ .
$\frac{-5}{2} \leq z$

STEP 6

Now we will solve the second part of the inequality, which is $2 z+5<8$ .

STEP 7

Subtract5 from both sides to isolate $z$ .
$2 z +5 -5 < -5$

STEP 8

implify the inequality.
$2z <3$

STEP 9

Divide both sides by2 to solve for $z$ .
$z < \frac{3}{2}$

STEP 10

Now we combine the two parts of the inequality to get the solution.
$\frac{-5}{2} \leq z < \frac{3}{2}$ So, $z$ is greater than or equal to $-5/2$ and less than $3/2$ .

Was this helpful?

QuestionSolve the inequality $0 \leq 2z + 5 < 8$ .

Studdy Solution

STEP 1

Assumptions1. The inequality is $0 \leq z+5<8$ . We are solving for $z$

STEP 2

The inequality is a compound inequality, meaning it has two parts. We will solve each part separately. The first part is $0 \leq2 z+5$ .

STEP 3

To isolate $z$ in the first part of the inequality, we need to subtract5 from both sides.
$0 -5 \leq2 z +5 -5$

STEP 4

implify the inequality.
$- \leq2z$

STEP 5

Next, divide both sides by2 to solve for $z$ .
$\frac{-5}{2} \leq z$

STEP 6

Now we will solve the second part of the inequality, which is $2 z+5<8$ .

STEP 7

Subtract5 from both sides to isolate $z$ .
$2 z +5 -5 < -5$

STEP 8

implify the inequality.
$2z <3$

STEP 9

Divide both sides by2 to solve for $z$ .
$z < \frac{3}{2}$

STEP 10

Now we combine the two parts of the inequality to get the solution.
$\frac{-5}{2} \leq z < \frac{3}{2}$ So, $z$ is greater than or equal to $-5/2$ and less than $3/2$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the inequality 0≤2z+5<80 \leq 2z + 5 < 80≤2z+5<8.

Studdy Solution

STEP 1

Assumptions1. The inequality is 0≤z+5<80 \leq z+5<80≤z+5<8 . We are solving for zzz

STEP 2

The inequality is a compound inequality, meaning it has two parts. We will solve each part separately. The first part is 0≤2z+50 \leq2 z+50≤2z+5.

STEP 3

To isolate zzz in the first part of the inequality, we need to subtract5 from both sides.0−5≤2z+5−50 -5 \leq2 z +5 -50−5≤2z+5−5

STEP 4

implify the inequality.−≤2z- \leq2z−≤2z

STEP 5

Next, divide both sides by2 to solve for zzz.−52≤z\frac{-5}{2} \leq z2−5​≤z

STEP 6

Now we will solve the second part of the inequality, which is 2z+5<82 z+5<82z+5<8.

STEP 7

Subtract5 from both sides to isolate zzz.2z+5−5<−52 z +5 -5 < -52z+5−5<−5

STEP 8

implify the inequality.2z<32z <32z<3

STEP 9

Divide both sides by2 to solve for zzz.z<32z < \frac{3}{2}z<23​

STEP 10

Now we combine the two parts of the inequality to get the solution.−52≤z<32\frac{-5}{2} \leq z < \frac{3}{2}2−5​≤z<23​So, zzz is greater than or equal to −5/2-5/2−5/2 and less than 3/23/23/2.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the inequality $0 \leq 2z + 5 < 8$ .

Assumptions1. The inequality is $0 \leq z+5<8$ . We are solving for $z$

The inequality is a compound inequality, meaning it has two parts. We will solve each part separately. The first part is $0 \leq2 z+5$ .

To isolate $z$ in the first part of the inequality, we need to subtract5 from both sides.
$0 -5 \leq2 z +5 -5$

implify the inequality.
$- \leq2z$

Next, divide both sides by2 to solve for $z$ .
$\frac{-5}{2} \leq z$

Now we will solve the second part of the inequality, which is $2 z+5<8$ .

Subtract5 from both sides to isolate $z$ .
$2 z +5 -5 < -5$

implify the inequality.
$2z <3$

Divide both sides by2 to solve for $z$ .
$z < \frac{3}{2}$

Now we combine the two parts of the inequality to get the solution.
$\frac{-5}{2} \leq z < \frac{3}{2}$ So, $z$ is greater than or equal to $-5/2$ and less than $3/2$ .