Question Solve the following linear equations, showing your work. 1) $15-2x=3x$ 2) $26-4x=9x$ 3) $5x-9=2x+12$ 4) $8x+10=35+3x$ 5) $5x+16=6-5x$

Studdy Solution

STEP 1

Assumptions
1. We are given five separate linear equations to solve for the variable $x$ .
2. We will solve each equation by isolating $x$ on one side of the equation.
3. After finding the value of $x$ , we will plug it back into the original equation to verify the solution.

STEP 2

Solve the first equation $15 - 2x = 3x$ .

STEP 3

Add $2x$ to both sides of the equation to bring all the $x$ terms to one side.
$15 - 2x + 2x = 3x + 2x$

STEP 4

Combine like terms.
$15 = 5x$

STEP 5

Divide both sides by $5$ to solve for $x$ .
$\frac{15}{5} = \frac{5x}{5}$

STEP 6

Calculate the value of $x$ .
$x = 3$

STEP 7

Plug $x = 3$ back into the original equation to verify the solution.
$15 - 2(3) \stackrel{?}{=} 3(3)$

STEP 8

Perform the multiplication.
$15 - 6 \stackrel{?}{=} 9$

STEP 9

Subtract $6$ from $15$ .
$9 = 9$

STEP 10

Since both sides are equal, the solution $x = 3$ is verified for the first equation.

STEP 11

Solve the second equation $26 - 4x = 9x$ .

STEP 12

Add $4x$ to both sides of the equation to bring all the $x$ terms to one side.
$26 - 4x + 4x = 9x + 4x$

STEP 13

Combine like terms.
$26 = 13x$

STEP 14

Divide both sides by $13$ to solve for $x$ .
$\frac{26}{13} = \frac{13x}{13}$

STEP 15

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

STEP 16

Plug $x = 2$ back into the original equation to verify the solution.
$26 - 4(2) \stackrel{?}{=} 9(2)$

STEP 17

Perform the multiplication.
$26 - 8 \stackrel{?}{=} 18$

STEP 18

Subtract $8$ from $26$ .
$18 = 18$

STEP 19

Since both sides are equal, the solution $x = 2$ is verified for the second equation.

STEP 20

Solve the third equation $5x - 9 = 2x + 12$ .

STEP 21

Subtract $2x$ from both sides of the equation to bring all the $x$ terms to one side.
$5x - 9 - 2x = 2x + 12 - 2x$

STEP 22

Combine like terms.
$3x - 9 = 12$

STEP 23

Add $9$ to both sides of the equation to isolate the term with $x$ .
$3x - 9 + 9 = 12 + 9$

STEP 24

Calculate the value on the right side.
$3x = 21$

STEP 25

Divide both sides by $3$ to solve for $x$ .
$\frac{3x}{3} = \frac{21}{3}$

STEP 26

Calculate the value of $x$ .
$x = 7$

STEP 27

Plug $x = 7$ back into the original equation to verify the solution.
$5(7) - 9 \stackrel{?}{=} 2(7) + 12$

STEP 28

Perform the multiplication.
$35 - 9 \stackrel{?}{=} 14 + 12$

STEP 29

Calculate the values on both sides.
$26 = 26$

STEP 30

Since both sides are equal, the solution $x = 7$ is verified for the third equation.

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