Solved on Feb 10, 2024

Solve the linear equation $2(5x+4) = 4(x+3) + 4 + 2x$ and select the correct solution.

STEP 1

Assumptions
1. We are given the equation $2(5x + 4) = 4(x + 3) + 4 + 2x$ .
2. We need to solve for $x$ .

STEP 2

First, we need to distribute the multiplication over addition on both sides of the equation.
For the left side, we distribute the $2$ across $5x + 4$ :
$2(5x + 4) = 2 \cdot 5x + 2 \cdot 4$

STEP 3

Now, perform the multiplication on the left side:
$2 \cdot 5x = 10x$ $2 \cdot 4 = 8$
So, we have:
$2(5x + 4) = 10x + 8$

STEP 4

For the right side, we distribute the $4$ across $x + 3$ :
$4(x + 3) = 4 \cdot x + 4 \cdot 3$

STEP 5

Now, perform the multiplication on the right side:
$4 \cdot x = 4x$ $4 \cdot 3 = 12$
So, we have:
$4(x + 3) = 4x + 12$

STEP 6

Combine the terms on the right side of the equation:
$4(x + 3) + 4 + 2x = 4x + 12 + 4 + 2x$

STEP 7

Now, add the constants on the right side:
$4x + 12 + 4 + 2x = 4x + 2x + 12 + 4$

STEP 8

Combine like terms on the right side:
$4x + 2x = 6x$ $12 + 4 = 16$
So, we have:
$4x + 12 + 4 + 2x = 6x + 16$

STEP 9

Now, we rewrite the original equation with the simplified terms:
$10x + 8 = 6x + 16$

STEP 10

Next, we will move all terms containing $x$ to one side and constants to the other side. Subtract $6x$ from both sides:
$10x + 8 - 6x = 6x + 16 - 6x$

STEP 11

Combine like terms:
$10x - 6x = 4x$
So, we have:
$4x + 8 = 16$

STEP 12

Now, subtract $8$ from both sides to isolate the term with $x$ :
$4x + 8 - 8 = 16 - 8$

STEP 13

Simplify both sides:
$4x = 8$

STEP 14

Finally, divide both sides by $4$ to solve for $x$ :
$\frac{4x}{4} = \frac{8}{4}$

STEP 15

Calculate the value of $x$ :
$x = 2$
The solution to the equation is $x = 2$ , which corresponds to option f.

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Solve the linear equation $2(5x+4) = 4(x+3) + 4 + 2x$ and select the correct solution.

STEP 1

Assumptions
1. We are given the equation $2(5x + 4) = 4(x + 3) + 4 + 2x$ .
2. We need to solve for $x$ .

STEP 2

First, we need to distribute the multiplication over addition on both sides of the equation.
For the left side, we distribute the $2$ across $5x + 4$ :
$2(5x + 4) = 2 \cdot 5x + 2 \cdot 4$

STEP 3

Now, perform the multiplication on the left side:
$2 \cdot 5x = 10x$ $2 \cdot 4 = 8$
So, we have:
$2(5x + 4) = 10x + 8$

STEP 4

For the right side, we distribute the $4$ across $x + 3$ :
$4(x + 3) = 4 \cdot x + 4 \cdot 3$

STEP 5

Now, perform the multiplication on the right side:
$4 \cdot x = 4x$ $4 \cdot 3 = 12$
So, we have:
$4(x + 3) = 4x + 12$

STEP 6

Combine the terms on the right side of the equation:
$4(x + 3) + 4 + 2x = 4x + 12 + 4 + 2x$

STEP 7

Now, add the constants on the right side:
$4x + 12 + 4 + 2x = 4x + 2x + 12 + 4$

STEP 8

Combine like terms on the right side:
$4x + 2x = 6x$ $12 + 4 = 16$
So, we have:
$4x + 12 + 4 + 2x = 6x + 16$

STEP 9

Now, we rewrite the original equation with the simplified terms:
$10x + 8 = 6x + 16$

STEP 10

Next, we will move all terms containing $x$ to one side and constants to the other side. Subtract $6x$ from both sides:
$10x + 8 - 6x = 6x + 16 - 6x$

STEP 11

Combine like terms:
$10x - 6x = 4x$
So, we have:
$4x + 8 = 16$

STEP 12

Now, subtract $8$ from both sides to isolate the term with $x$ :
$4x + 8 - 8 = 16 - 8$

STEP 13

Simplify both sides:
$4x = 8$

STEP 14

Finally, divide both sides by $4$ to solve for $x$ :
$\frac{4x}{4} = \frac{8}{4}$

STEP 15

Calculate the value of $x$ :
$x = 2$
The solution to the equation is $x = 2$ , which corresponds to option f.

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Solve the linear equation 2(5x+4)=4(x+3)+4+2x2(5x+4) = 4(x+3) + 4 + 2x2(5x+4)=4(x+3)+4+2x and select the correct solution.

STEP 1

Assumptions1. We are given the equation 2(5x+4)=4(x+3)+4+2x2(5x + 4) = 4(x + 3) + 4 + 2x2(5x+4)=4(x+3)+4+2x.2. We need to solve for xxx.

STEP 2

First, we need to distribute the multiplication over addition on both sides of the equation.For the left side, we distribute the 222 across 5x+45x + 45x+4:2(5x+4)=2⋅5x+2⋅42(5x + 4) = 2 \cdot 5x + 2 \cdot 42(5x+4)=2⋅5x+2⋅4

STEP 3

Now, perform the multiplication on the left side:2⋅5x=10x2 \cdot 5x = 10x2⋅5x=10x 2⋅4=82 \cdot 4 = 82⋅4=8So, we have:2(5x+4)=10x+82(5x + 4) = 10x + 82(5x+4)=10x+8

STEP 4

For the right side, we distribute the 444 across x+3x + 3x+3:4(x+3)=4⋅x+4⋅34(x + 3) = 4 \cdot x + 4 \cdot 34(x+3)=4⋅x+4⋅3

STEP 5

Now, perform the multiplication on the right side:4⋅x=4x4 \cdot x = 4x4⋅x=4x 4⋅3=124 \cdot 3 = 124⋅3=12So, we have:4(x+3)=4x+124(x + 3) = 4x + 124(x+3)=4x+12

STEP 6

Combine the terms on the right side of the equation:4(x+3)+4+2x=4x+12+4+2x4(x + 3) + 4 + 2x = 4x + 12 + 4 + 2x4(x+3)+4+2x=4x+12+4+2x

STEP 7

Now, add the constants on the right side:4x+12+4+2x=4x+2x+12+44x + 12 + 4 + 2x = 4x + 2x + 12 + 44x+12+4+2x=4x+2x+12+4

STEP 8

Combine like terms on the right side:4x+2x=6x4x + 2x = 6x4x+2x=6x 12+4=1612 + 4 = 1612+4=16So, we have:4x+12+4+2x=6x+164x + 12 + 4 + 2x = 6x + 164x+12+4+2x=6x+16

STEP 9

Now, we rewrite the original equation with the simplified terms:10x+8=6x+1610x + 8 = 6x + 1610x+8=6x+16

STEP 10

Next, we will move all terms containing xxx to one side and constants to the other side. Subtract 6x6x6x from both sides:10x+8−6x=6x+16−6x10x + 8 - 6x = 6x + 16 - 6x10x+8−6x=6x+16−6x

STEP 11

Combine like terms:10x−6x=4x10x - 6x = 4x10x−6x=4xSo, we have:4x+8=164x + 8 = 164x+8=16

STEP 12

Now, subtract 888 from both sides to isolate the term with xxx:4x+8−8=16−84x + 8 - 8 = 16 - 84x+8−8=16−8

STEP 13

Simplify both sides:4x=84x = 84x=8

STEP 14

Finally, divide both sides by 444 to solve for xxx:4x4=84\frac{4x}{4} = \frac{8}{4}44x​=48​

STEP 15

Calculate the value of xxx:x=2x = 2x=2The solution to the equation is x=2x = 2x=2, which corresponds to option f.

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Solve the linear equation $2(5x+4) = 4(x+3) + 4 + 2x$ and select the correct solution.

Assumptions
1. We are given the equation $2(5x + 4) = 4(x + 3) + 4 + 2x$ .
2. We need to solve for $x$ .

First, we need to distribute the multiplication over addition on both sides of the equation.
For the left side, we distribute the $2$ across $5x + 4$ :
$2(5x + 4) = 2 \cdot 5x + 2 \cdot 4$

Now, perform the multiplication on the left side:
$2 \cdot 5x = 10x$ $2 \cdot 4 = 8$
So, we have:
$2(5x + 4) = 10x + 8$

For the right side, we distribute the $4$ across $x + 3$ :
$4(x + 3) = 4 \cdot x + 4 \cdot 3$

Now, perform the multiplication on the right side:
$4 \cdot x = 4x$ $4 \cdot 3 = 12$
So, we have:
$4(x + 3) = 4x + 12$

Combine the terms on the right side of the equation:
$4(x + 3) + 4 + 2x = 4x + 12 + 4 + 2x$

Now, add the constants on the right side:
$4x + 12 + 4 + 2x = 4x + 2x + 12 + 4$

Combine like terms on the right side:
$4x + 2x = 6x$ $12 + 4 = 16$
So, we have:
$4x + 12 + 4 + 2x = 6x + 16$

Now, we rewrite the original equation with the simplified terms:
$10x + 8 = 6x + 16$

Next, we will move all terms containing $x$ to one side and constants to the other side. Subtract $6x$ from both sides:
$10x + 8 - 6x = 6x + 16 - 6x$

Combine like terms:
$10x - 6x = 4x$
So, we have:
$4x + 8 = 16$

Now, subtract $8$ from both sides to isolate the term with $x$ :
$4x + 8 - 8 = 16 - 8$

Simplify both sides:
$4x = 8$

Finally, divide both sides by $4$ to solve for $x$ :
$\frac{4x}{4} = \frac{8}{4}$

Calculate the value of $x$ :
$x = 2$
The solution to the equation is $x = 2$ , which corresponds to option f.