QuestionSolve for $a$ in the equation: $-16-7(2 a+3)=23-2 a$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $-16-7( a+3)=23- a$ . We are solving for the variable $a$

STEP 2

First, we need to distribute the $-7$ across the $(2 a+)$ on the left side of the equation.
$-16-7(2 a+) = -16 -7 \cdot2a -7 \cdot$

STEP 3

Now, calculate the multiplication.
$-16 -14a -21 =23 -2a$

STEP 4

Combine like terms on the left side of the equation.
$-37 -14a =23 -2a$

STEP 5

Rearrange the equation to isolate the variable terms on one side and constant terms on the other.
$-14a +2a =23 +37$

STEP 6

Combine like terms on both sides of the equation.
$-12a =60$

STEP 7

To solve for $a$ , divide both sides of the equation by $-12$ .
$a = \frac{60}{-12}$

STEP 8

Calculate the value of $a$ .
$a = -5$ So, the solution to the equation $-16-7(2 a+3)=23-2 a$ is $a = -5$ .

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QuestionSolve for $a$ in the equation: $-16-7(2 a+3)=23-2 a$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $-16-7( a+3)=23- a$ . We are solving for the variable $a$

STEP 2

First, we need to distribute the $-7$ across the $(2 a+)$ on the left side of the equation.
$-16-7(2 a+) = -16 -7 \cdot2a -7 \cdot$

STEP 3

Now, calculate the multiplication.
$-16 -14a -21 =23 -2a$

STEP 4

Combine like terms on the left side of the equation.
$-37 -14a =23 -2a$

STEP 5

Rearrange the equation to isolate the variable terms on one side and constant terms on the other.
$-14a +2a =23 +37$

STEP 6

Combine like terms on both sides of the equation.
$-12a =60$

STEP 7

To solve for $a$ , divide both sides of the equation by $-12$ .
$a = \frac{60}{-12}$

STEP 8

Calculate the value of $a$ .
$a = -5$ So, the solution to the equation $-16-7(2 a+3)=23-2 a$ is $a = -5$ .

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QuestionSolve for aaa in the equation: −16−7(2a+3)=23−2a-16-7(2 a+3)=23-2 a−16−7(2a+3)=23−2a.

Studdy Solution

STEP 1

Assumptions1. The equation is −16−7(a+3)=23−a-16-7( a+3)=23- a−16−7(a+3)=23−a . We are solving for the variable aaa

STEP 2

First, we need to distribute the −7-7−7 across the (2a+)(2 a+)(2a+) on the left side of the equation.−16−7(2a+)=−16−7⋅2a−7⋅-16-7(2 a+) = -16 -7 \cdot2a -7 \cdot−16−7(2a+)=−16−7⋅2a−7⋅

STEP 3

Now, calculate the multiplication.−16−14a−21=23−2a-16 -14a -21 =23 -2a−16−14a−21=23−2a

STEP 4

Combine like terms on the left side of the equation.−37−14a=23−2a-37 -14a =23 -2a−37−14a=23−2a

STEP 5

Rearrange the equation to isolate the variable terms on one side and constant terms on the other.−14a+2a=23+37-14a +2a =23 +37−14a+2a=23+37

STEP 6

Combine like terms on both sides of the equation.−12a=60-12a =60−12a=60

STEP 7

To solve for aaa, divide both sides of the equation by −12-12−12.a=60−12a = \frac{60}{-12}a=−1260​

STEP 8

Calculate the value of aaa.a=−5a = -5a=−5So, the solution to the equation −16−7(2a+3)=23−2a-16-7(2 a+3)=23-2 a−16−7(2a+3)=23−2a is a=−5a = -5a=−5.

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QuestionSolve for $a$ in the equation: $-16-7(2 a+3)=23-2 a$ .

Assumptions1. The equation is $-16-7( a+3)=23- a$ . We are solving for the variable $a$

First, we need to distribute the $-7$ across the $(2 a+)$ on the left side of the equation.
$-16-7(2 a+) = -16 -7 \cdot2a -7 \cdot$

Now, calculate the multiplication.
$-16 -14a -21 =23 -2a$

Combine like terms on the left side of the equation.
$-37 -14a =23 -2a$

Rearrange the equation to isolate the variable terms on one side and constant terms on the other.
$-14a +2a =23 +37$

Combine like terms on both sides of the equation.
$-12a =60$

To solve for $a$ , divide both sides of the equation by $-12$ .
$a = \frac{60}{-12}$

Calculate the value of $a$ .
$a = -5$ So, the solution to the equation $-16-7(2 a+3)=23-2 a$ is $a = -5$ .