Solving Linear Equations Unit Test
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Question
Solve the following linear equation for x. Then check your answer. Show all your steps for solving and checking.
5x+8+x=32
(4 points)
To solve the equation 5x + 8 + x = 32, we will combine like terms and isolate the variable x.
First, combine the terms with x:
5x + x = 6x
The equation now becomes:
6x + 8 = 32
Next, we will isolate the variable 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 will divide both sides of the equation by 6:
(6x)/6 = 24/6
This simplifies to:
x = 4
To check if our answer is correct, we substitute the value of x back into the original equation:
5x + 8 + x = 32
Substituting x = 4:
5(4) + 8 + 4 = 32
20 + 8 + 4 = 32
32 = 32
Since both sides of the equation are equal, our solution x = 4 is correct.
To solve the equation 5x + 8 + x = 32 for x, we need to combine the like terms on the left side of the equation.
Step 1: Combine like terms
5x + x = 32 - 8
6x = 24
Step 2: Divide both sides by 6 to isolate x
6x/6 = 24/6
x = 4
So, the solution to the equation 5x + 8 + x = 32 is x = 4.
To check if our answer is correct, substitute the value of x back into the original equation and see if it holds true.
Original equation: 5x + 8 + x = 32
Substituting x = 4: 5(4) + 8 + 4 = 32
20 + 8 + 4 = 32
32 = 32
Since both sides of the equation are equal, our solution x = 4 is correct.
To solve the given linear equation 5x + 8 + x = 32, we need to isolate the variable x on one side of the equation.
Step 1: Combine like terms
The equation can be simplified by combining the terms that have the same variable, which in this case is x. So, 5x + x can be simplified to 6x.
6x + 8 = 32
Step 2: Eliminate the constant term
Next, we need to eliminate the constant term, which is 8, by subtracting it from both sides of the equation:
6x + 8 - 8 = 32 - 8
This simplifies to:
6x = 24
Step 3: Solve for x
To solve for x, we need to isolate it. In this case, we have 6x = 24. To isolate x, divide both sides of the equation by the coefficient of x, which is 6:
(6x)/6 = 24/6
This gives us:
x = 4
So, the solution to the equation 5x + 8 + x = 32 is x = 4.
Step 4: Check the answer
To check if our solution is correct, substitute the value of x back into the original equation and see if both sides are equal.
5(4) + 8 + 4 = 32
20 + 8 + 4 = 32
32 = 32
Since both sides of the equation are equal, our solution x = 4 is correct.
Therefore, x = 4 is the solution to the linear equation 5x + 8 + x = 32.