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Question Solve the linear equation 2x+5=−3x+102x + 5 = -3x + 10 for the unknown variable xx.

Studdy Solution

STEP 1

Assumptions
1. We are given a linear equation in one variable: 2x+5=−3x+102x + 5 = -3x + 10.
2. We need to find the value of xx that satisfies the equation.

STEP 2

The first step is to collect like terms. We want to move all terms containing xx to one side of the equation and the constant terms to the other side. We can do this by adding 3x3x to both sides of the equation to move the xx-terms to the left side and by subtracting 55 from both sides to move the constant terms to the right side.
2x+5+3x−5=−3x+10+3x−52x + 5 + 3x - 5 = -3x + 10 + 3x - 5

STEP 3

Now, simplify both sides of the equation by combining like terms.
(2x+3x)+(5−5)=(−3x+3x)+(10−5) (2x + 3x) + (5 - 5) = (-3x + 3x) + (10 - 5)

STEP 4

Perform the addition and subtraction.
5x+0=0+5 5x + 0 = 0 + 5

STEP 5

The equation simplifies to:
5x=5 5x = 5

STEP 6

To find the value of xx, we now divide both sides of the equation by 55, which is the coefficient of xx.
5x5=55 \frac{5x}{5} = \frac{5}{5}

STEP 7

Simplify both sides of the equation to solve for xx.
x=1 x = 1
The value of xx that satisfies the equation 2x+5=−3x+102x + 5 = -3x + 10 is x=1x = 1.

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