Solved on Jan 23, 2024

Solve the linear equation $x=4(8+5x)$ for the value of $x$ .

STEP 1

Assumptions
1. Solve the equation for the variable $x$ .
2. Apply the distributive property to the right side of the equation.
3. Combine like terms.
4. Isolate the variable $x$ on one side of the equation.

STEP 2

Apply the distributive property to the right side of the equation to eliminate the parentheses.
$x = 4 \cdot 8 + 4 \cdot 5x$

STEP 3

Perform the multiplication.
$x = 32 + 20x$

STEP 4

Subtract $20x$ from both sides of the equation to start isolating the variable $x$ .
$x - 20x = 32 + 20x - 20x$

STEP 5

Combine like terms on both sides of the equation.
$-19x = 32$

STEP 6

Divide both sides of the equation by $-19$ to solve for $x$ .
$x = \frac{32}{-19}$

STEP 7

Simplify the fraction if possible.
$x = -\frac{32}{19}$
The solution to the equation is $x = -\frac{32}{19}$ .

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Solve the linear equation $x=4(8+5x)$ for the value of $x$ .

STEP 1

Assumptions
1. Solve the equation for the variable $x$ .
2. Apply the distributive property to the right side of the equation.
3. Combine like terms.
4. Isolate the variable $x$ on one side of the equation.

STEP 2

Apply the distributive property to the right side of the equation to eliminate the parentheses.
$x = 4 \cdot 8 + 4 \cdot 5x$

STEP 3

Perform the multiplication.
$x = 32 + 20x$

STEP 4

Subtract $20x$ from both sides of the equation to start isolating the variable $x$ .
$x - 20x = 32 + 20x - 20x$

STEP 5

Combine like terms on both sides of the equation.
$-19x = 32$

STEP 6

Divide both sides of the equation by $-19$ to solve for $x$ .
$x = \frac{32}{-19}$

STEP 7

Simplify the fraction if possible.
$x = -\frac{32}{19}$
The solution to the equation is $x = -\frac{32}{19}$ .

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Solve the linear equation x=4(8+5x)x=4(8+5x)x=4(8+5x) for the value of xxx.

STEP 1

Assumptions1. Solve the equation for the variable xxx.2. Apply the distributive property to the right side of the equation.3. Combine like terms.4. Isolate the variable xxx on one side of the equation.

STEP 2

Apply the distributive property to the right side of the equation to eliminate the parentheses.x=4⋅8+4⋅5xx = 4 \cdot 8 + 4 \cdot 5xx=4⋅8+4⋅5x

STEP 3

Perform the multiplication.x=32+20xx = 32 + 20xx=32+20x

STEP 4

Subtract 20x20x20x from both sides of the equation to start isolating the variable xxx.x−20x=32+20x−20xx - 20x = 32 + 20x - 20xx−20x=32+20x−20x

STEP 5

Combine like terms on both sides of the equation.−19x=32-19x = 32−19x=32

STEP 6

Divide both sides of the equation by −19-19−19 to solve for xxx.x=32−19x = \frac{32}{-19}x=−1932​

STEP 7

Simplify the fraction if possible.x=−3219x = -\frac{32}{19}x=−1932​The solution to the equation is x=−3219x = -\frac{32}{19}x=−1932​.

Start learning now

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

Solve the linear equation $x=4(8+5x)$ for the value of $x$ .

Assumptions
1. Solve the equation for the variable $x$ .
2. Apply the distributive property to the right side of the equation.
3. Combine like terms.
4. Isolate the variable $x$ on one side of the equation.

Apply the distributive property to the right side of the equation to eliminate the parentheses.
$x = 4 \cdot 8 + 4 \cdot 5x$

Perform the multiplication.
$x = 32 + 20x$

Subtract $20x$ from both sides of the equation to start isolating the variable $x$ .
$x - 20x = 32 + 20x - 20x$

Combine like terms on both sides of the equation.
$-19x = 32$

Divide both sides of the equation by $-19$ to solve for $x$ .
$x = \frac{32}{-19}$

Simplify the fraction if possible.
$x = -\frac{32}{19}$
The solution to the equation is $x = -\frac{32}{19}$ .