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Math  /  Algebra

Question2(3x+5)=10+4(2x−3)2(3 x+5)=10+4(2 x-3)
Use the keypad to enter the answer in the box. x=x=

Studdy Solution

STEP 1

1. The equation 2(3x+5)=10+4(2x−3) 2(3x + 5) = 10 + 4(2x - 3) is a linear equation.
2. The goal is to solve for the variable x x .
3. The equation involves distributing, combining like terms, and isolating the variable.

STEP 2

1. Expand both sides of the equation.
2. Simplify and combine like terms.
3. Isolate the variable x x .
4. Solve for x x .

STEP 3

Expand both sides of the equation using the distributive property.
Left side: 2(3x+5)=6x+10 2(3x + 5) = 6x + 10
Right side: 4(2x−3)=8x−12 4(2x - 3) = 8x - 12
The equation now becomes: 6x+10=10+8x−12 6x + 10 = 10 + 8x - 12

STEP 4

Simplify the right side of the equation by combining like terms:
10−12=−2 10 - 12 = -2
The equation now becomes: 6x+10=8x−2 6x + 10 = 8x - 2

STEP 5

Move all terms involving x x to one side and constant terms to the other side.
Subtract 6x 6x from both sides: 10=2x−2 10 = 2x - 2
Add 2 to both sides to isolate terms with x x : 12=2x 12 = 2x

STEP 6

Solve for x x by dividing both sides by 2:
x=122 x = \frac{12}{2}
Simplify: x=6 x = 6
The solution is: x=6 x = 6

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