Solve the following linear equation for x. Then check your answer. Show all your steps for solving and checking.
5x + 8 + x = 32
To solve the equation 5x + 8 + x = 32, we first need to combine like terms.
Combining the x terms: 5x + x = 6x
The equation then becomes: 6x + 8 = 32
Next, we want to isolate x by subtracting 8 from both sides of the equation.
6x + 8 - 8 = 32 - 8
This simplifies to: 6x = 24
To solve for x, we divide both sides of the equation by 6:
6x/6 = 24/6
This simplifies to: x = 4
To check our answer, we substitute x = 4 back into the original equation:
5(4) + 8 + 4 = 32
20 + 8 + 4 = 32
32 = 32
Since both sides of the equation are equal, we can conclude that x = 4 is the correct solution.
Step 1: Combine like terms on the left side of the equation.
5x + 8 + x = 32
6x + 8 = 32
Step 2: Simplify the equation by subtracting 8 from both sides of the equation.
6x + 8 - 8 = 32 - 8
6x = 24
Step 3: Divide both sides of the equation by 6 to solve for x.
6x/6 = 24/6
x = 4
Step 4: Check the solution by substituting the value of x back into the original equation.
5x + 8 + x = 32
5(4) + 8 + 4 = 32
20 + 8 + 4 = 32
32 = 32
Therefore, the solution is x = 4 and it checks out when substituted into the original equation.
To solve the given linear equation, we will follow these steps:
Step 1: Simplify the equation.
Step 2: Combine like terms.
Step 3: Isolate the variable term.
Step 4: Solve for the variable.
Step 5: Check the solution by substituting it back into the original equation.
Let's begin:
Step 1: Simplify the equation.
5x + 8 + x = 32
Step 2: Combine like terms.
Combine the x terms on the left side of the equation.
5x + x + 8 = 32
Step 3: Isolate the variable term.
Combine the x terms. On the left side of the equation, 5x + x becomes 6x.
6x + 8 = 32
Step 4: Solve for the variable.
To isolate the variable, we need to undo the addition of 8 from the left side of the equation. We can do this by subtracting 8 from both sides.
6x + 8 - 8 = 32 - 8
6x = 24
To solve for x, divide both sides of the equation by 6.
(6x)/6 = 24/6
x = 4
Step 5: Check the solution by substituting it back into the original equation.
Let's substitute x = 4 into the equation:
5x + 8 + x = 32
5(4) + 8 + 4 = 32
20 + 8 + 4 = 32
32 = 32
The left side of the equation is equal to the right side, which means our solution is correct.
Therefore, the given linear equation 5x + 8 + x = 32 is solved, and the solution is x = 4.