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QuestionSolve the equations: a. 5x−2=85x - 2 = 8, b. 4x−3=2x+94x - 3 = 2x + 9, c. 6x+3=2x+86x + 3 = 2x + 8.

Studdy Solution

STEP 1

Assumptions1. The equations are linear equations in one variable. . The variable in each equation is x.
3. The goal is to solve for x in each equation.

STEP 2

Let's start with the first equation 5x−2=85 x-2=8. We need to isolate x. We can do this by adding2 to both sides of the equation.
5x−2+2=8+25 x-2+2=8+2

STEP 3

implify the equation.
5x=105 x =10

STEP 4

Now, divide both sides of the equation by to solve for x.
x=10x = \frac{10}{}

STEP 5

Calculate the value of x.
x=2x =2

STEP 6

Now, let's move to the second equation 4x−3=2x+94 x-3=2 x+9. First, we need to get all terms with x on one side of the equation and the constants on the other side. We can do this by subtracting 2x2x from both sides.
4x−2x=2x−2x+9+34 x -2 x =2 x -2 x +9 +3

STEP 7

implify the equation.
2x=122 x =12

STEP 8

Now, divide both sides of the equation by2 to solve for x.
x=122x = \frac{12}{2}

STEP 9

Calculate the value of x.
x=6x =6

STEP 10

Finally, let's solve the third equation 6x+3=2x+86 x+3=2 x+8. First, we need to get all terms with x on one side of the equation and the constants on the other side. We can do this by subtracting 2x2x and 33 from both sides.
6x−2x=2x−2x+8−36 x -2 x =2 x -2 x +8 -3

STEP 11

implify the equation.
4x=54 x =5

STEP 12

Now, divide both sides of the equation by4 to solve for x.
x=54x = \frac{5}{4}

STEP 13

Calculate the value of x.
x=.25x =.25The solutions to the equations are x=2x =2, x=6x =6, and x=.25x =.25.

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