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3x + 4 = 7

Solving a linear equation refers to the process of determining the solution set.
Given the equation 3x + 4 = 7, will there ever be more than one solution for x?
What is the solution to this equation? Show all work.

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1 Answer

Whenever you have an equation with a plain variable (that is, no exponent included), there is only one number that will work when substituted for x.

To solve it, you have to "undo" what is done to the variable. You also go in the reverse order of operations, so you do the addition/subtract first, then multiplication/division.

You also have to do the same to both sides, kind of like keeping a balance scale in balance.

In this case, we subtract 4 from both sides first:

3x + 4 -4 = 7 - 4

The + 4 - 4 cancel each other out, so you get:

3x = 3

3x means "3 times x" so you divide by 3 to undo it. I will use the / to indicate division:

3x / 3 = 3 /3 

so 1x = 1.

Since 1x is "1 times x" it is the same as x by itself, so:

x=1

AND, if we substitute 1 back into the original equation (the asterisk stands for multiply):

3 * 1 + 4 = 7

3 * 1 is 3, so:

3 + 4 = 7     which is true.

1 is the only number that works.

Hope this helped.

Kathye P.

Houston, TX

Comments

Hi Kathye, Thank you so much. I was on the right track, but your explanation clearly explained the process. Pam

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