Question Solve the linear equation $6(a + 3.9) = 19.56$ using a different method. Show the steps.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $6(a+3.9)=19.56$ .
2. We need to solve for the variable $a$ .
3. We will use algebraic manipulation to isolate $a$ .

STEP 2

First, we will distribute the $6$ across the parentheses to simplify the left side of the equation.
$6(a+3.9) = 6 \cdot a + 6 \cdot 3.9$

STEP 3

Now, perform the multiplication to find the terms.
$6 \cdot a + 6 \cdot 3.9 = 6a + 23.4$

STEP 4

Rewrite the original equation with the simplified left side.
$6a + 23.4 = 19.56$

STEP 5

Next, we will isolate the term containing $a$ by subtracting $23.4$ from both sides of the equation.
$6a + 23.4 - 23.4 = 19.56 - 23.4$

STEP 6

Perform the subtraction to simplify both sides of the equation.
$6a = 19.56 - 23.4$

STEP 7

Calculate the difference on the right side of the equation.
$6a = -3.84$

STEP 8

Now, to solve for $a$ , divide both sides of the equation by $6$ .
$\frac{6a}{6} = \frac{-3.84}{6}$

STEP 9

Perform the division to find the value of $a$ .
$a = \frac{-3.84}{6}$

STEP 10

Calculate the value of $a$ .
$a = -0.64$
The solution to the equation $6(a+3.9)=19.56$ is $a = -0.64$ .

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