Solved on Sep 28, 2023

Solve the inequality $2(k+5)>32$ for the value of $k$ .

STEP 1

Assumptions1. We are solving the inequality $(k+5)>32$ for the variable $k$ . . The operations of addition, multiplication, and division are allowed in inequalities, similar to equalities, with one exception when we multiply or divide by a negative number, the direction of the inequality sign changes.

STEP 2

First, we need to distribute the2 to both terms inside the parentheses.
$2(k+5) =2k +2 \cdot5$

STEP 3

Calculate the multiplication.
$2k +2 \cdot5 =2k +10$

STEP 4

Now, substitute this back into the inequality.
$2k +10 >32$

STEP 5

To isolate $k$ , we first subtract10 from both sides of the inequality.
$2k +10 -10 >32 -10$

STEP 6

Calculate the subtraction.
$2k >32 -10 =22$

STEP 7

Now, divide both sides of the inequality by2 to solve for $k$ .
$\frac{2k}{2} > \frac{22}{2}$

STEP 8

Calculate the division.
$k > \frac{22}{2} =11$ So, the solution to the inequality $2(k+5)>32$ is $k >11$ .

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Solve the inequality $2(k+5)>32$ for the value of $k$ .

STEP 1

STEP 2

First, we need to distribute the2 to both terms inside the parentheses.
$2(k+5) =2k +2 \cdot5$

STEP 3

Calculate the multiplication.
$2k +2 \cdot5 =2k +10$

STEP 4

Now, substitute this back into the inequality.
$2k +10 >32$

STEP 5

To isolate $k$ , we first subtract10 from both sides of the inequality.
$2k +10 -10 >32 -10$

STEP 6

Calculate the subtraction.
$2k >32 -10 =22$

STEP 7

Now, divide both sides of the inequality by2 to solve for $k$ .
$\frac{2k}{2} > \frac{22}{2}$

STEP 8

Calculate the division.
$k > \frac{22}{2} =11$ So, the solution to the inequality $2(k+5)>32$ is $k >11$ .

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Solve the inequality 2(k+5)>322(k+5)>322(k+5)>32 for the value of kkk.

STEP 1

STEP 2

First, we need to distribute the2 to both terms inside the parentheses.2(k+5)=2k+2⋅52(k+5) =2k +2 \cdot52(k+5)=2k+2⋅5

STEP 3

Calculate the multiplication.2k+2⋅5=2k+102k +2 \cdot5 =2k +102k+2⋅5=2k+10

STEP 4

Now, substitute this back into the inequality.2k+10>322k +10 >322k+10>32

STEP 5

To isolate kkk, we first subtract10 from both sides of the inequality.2k+10−10>32−102k +10 -10 >32 -102k+10−10>32−10

STEP 6

Calculate the subtraction.2k>32−10=222k >32 -10 =222k>32−10=22

STEP 7

Now, divide both sides of the inequality by2 to solve for kkk.2k2>222\frac{2k}{2} > \frac{22}{2}22k​>222​

STEP 8

Calculate the division.k>222=11k > \frac{22}{2} =11k>222​=11So, the solution to the inequality 2(k+5)>322(k+5)>322(k+5)>32 is k>11k >11k>11.

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Solve the inequality $2(k+5)>32$ for the value of $k$ .

First, we need to distribute the2 to both terms inside the parentheses.
$2(k+5) =2k +2 \cdot5$

Calculate the multiplication.
$2k +2 \cdot5 =2k +10$

Now, substitute this back into the inequality.
$2k +10 >32$

To isolate $k$ , we first subtract10 from both sides of the inequality.
$2k +10 -10 >32 -10$

Calculate the subtraction.
$2k >32 -10 =22$

Now, divide both sides of the inequality by2 to solve for $k$ .
$\frac{2k}{2} > \frac{22}{2}$

Calculate the division.
$k > \frac{22}{2} =11$ So, the solution to the inequality $2(k+5)>32$ is $k >11$ .