Solved on Jan 18, 2024

Find the value of $a$ that satisfies the equation $3(a+1.5)=-1.5$ .

STEP 1

Assumptions
1. We are given the equation $3(a+1.5)=-1.5$ .
2. We need to solve for the variable $a$ .
3. The possible values of $a$ are given as $-2$ , $-1$ , $2$ , and $1$ .

STEP 2

First, we need to distribute the $3$ across the terms inside the parentheses.
$3(a+1.5) = 3a + 3(1.5)$

STEP 3

Calculate the product of $3$ and $1.5$ .
$3(1.5) = 4.5$

STEP 4

Rewrite the equation with the distributed terms.
$3a + 4.5 = -1.5$

STEP 5

Next, we need to isolate the variable $a$ on one side of the equation. We can do this by subtracting $4.5$ from both sides of the equation.
$3a + 4.5 - 4.5 = -1.5 - 4.5$

STEP 6

Calculate the result of the subtraction on both sides.
$3a = -1.5 - 4.5$

STEP 7

Combine the numbers on the right side of the equation.
$3a = -6$

STEP 8

Now, divide both sides of the equation by $3$ to solve for $a$ .
$\frac{3a}{3} = \frac{-6}{3}$

STEP 9

Calculate the division to find the value of $a$ .
$a = -2$
The value of $a$ that makes the equation true is $-2$ .

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Find the value of $a$ that satisfies the equation $3(a+1.5)=-1.5$ .

STEP 1

Assumptions
1. We are given the equation $3(a+1.5)=-1.5$ .
2. We need to solve for the variable $a$ .
3. The possible values of $a$ are given as $-2$ , $-1$ , $2$ , and $1$ .

STEP 2

First, we need to distribute the $3$ across the terms inside the parentheses.
$3(a+1.5) = 3a + 3(1.5)$

STEP 3

Calculate the product of $3$ and $1.5$ .
$3(1.5) = 4.5$

STEP 4

Rewrite the equation with the distributed terms.
$3a + 4.5 = -1.5$

STEP 5

Next, we need to isolate the variable $a$ on one side of the equation. We can do this by subtracting $4.5$ from both sides of the equation.
$3a + 4.5 - 4.5 = -1.5 - 4.5$

STEP 6

Calculate the result of the subtraction on both sides.
$3a = -1.5 - 4.5$

STEP 7

Combine the numbers on the right side of the equation.
$3a = -6$

STEP 8

Now, divide both sides of the equation by $3$ to solve for $a$ .
$\frac{3a}{3} = \frac{-6}{3}$

STEP 9

Calculate the division to find the value of $a$ .
$a = -2$
The value of $a$ that makes the equation true is $-2$ .

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Find the value of aaa that satisfies the equation 3(a+1.5)=−1.53(a+1.5)=-1.53(a+1.5)=−1.5.

STEP 1

Assumptions1. We are given the equation 3(a+1.5)=−1.53(a+1.5)=-1.53(a+1.5)=−1.5.2. We need to solve for the variable aaa.3. The possible values of aaa are given as −2-2−2, −1-1−1, 222, and 111.

STEP 2

First, we need to distribute the 333 across the terms inside the parentheses.3(a+1.5)=3a+3(1.5)3(a+1.5) = 3a + 3(1.5)3(a+1.5)=3a+3(1.5)

STEP 3

Calculate the product of 333 and 1.51.51.5.3(1.5)=4.53(1.5) = 4.53(1.5)=4.5

STEP 4

Rewrite the equation with the distributed terms.3a+4.5=−1.53a + 4.5 = -1.53a+4.5=−1.5

STEP 5

Next, we need to isolate the variable aaa on one side of the equation. We can do this by subtracting 4.54.54.5 from both sides of the equation.3a+4.5−4.5=−1.5−4.53a + 4.5 - 4.5 = -1.5 - 4.53a+4.5−4.5=−1.5−4.5

STEP 6

Calculate the result of the subtraction on both sides.3a=−1.5−4.53a = -1.5 - 4.53a=−1.5−4.5

STEP 7

Combine the numbers on the right side of the equation.3a=−63a = -63a=−6

STEP 8

Now, divide both sides of the equation by 333 to solve for aaa.3a3=−63\frac{3a}{3} = \frac{-6}{3}33a​=3−6​

STEP 9

Calculate the division to find the value of aaa.a=−2a = -2a=−2The value of aaa that makes the equation true is −2-2−2.

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Find the value of $a$ that satisfies the equation $3(a+1.5)=-1.5$ .

Assumptions
1. We are given the equation $3(a+1.5)=-1.5$ .
2. We need to solve for the variable $a$ .
3. The possible values of $a$ are given as $-2$ , $-1$ , $2$ , and $1$ .

First, we need to distribute the $3$ across the terms inside the parentheses.
$3(a+1.5) = 3a + 3(1.5)$

Calculate the product of $3$ and $1.5$ .
$3(1.5) = 4.5$

Rewrite the equation with the distributed terms.
$3a + 4.5 = -1.5$

Next, we need to isolate the variable $a$ on one side of the equation. We can do this by subtracting $4.5$ from both sides of the equation.
$3a + 4.5 - 4.5 = -1.5 - 4.5$

Calculate the result of the subtraction on both sides.
$3a = -1.5 - 4.5$

Combine the numbers on the right side of the equation.
$3a = -6$

Now, divide both sides of the equation by $3$ to solve for $a$ .
$\frac{3a}{3} = \frac{-6}{3}$

Calculate the division to find the value of $a$ .
$a = -2$
The value of $a$ that makes the equation true is $-2$ .