   SEARCH HOME Math Central Quandaries & Queries  Question from Nikko, a student: HELP please how do I solve these type of questions? 3x +5= 4x-10 or 4x +10= 6x-8 Hi Nikko,

I'll solve 4x - 5 = 7 + x which is similar. What you need to do is to manipulate the equation, always maintaining that the two sides are equal, and end with an equation looking like x = some number. There are two manipulations you can perform that will maintain the equality. You can add the same amount to each side and you can multiply both sides by the same amount.

Look at my equation,

4x - 5 = 7 + x.

I want to end with x = some number so I don't want the x on the right side of the equality. To eliminate the x on the right side I add -x to both sides.

4x - 5 - x = 7 + x - x.

This simplifies to

3x - 5 = 7.

Again my goal is x = some number so I don't want the -5 on the left of the equal sign. To eliminate -5 from the left I add 5 to both sides

3x - 5 + 5 = 7 + 5

which simplifies to

3x = 12.

Almost there, I want x on the left not 3x, so what I do is multiply both sides by 1/3.

1/3 × 3x = 1/3 × 12

which finally simplifies to

x = 4.

You can check that this answer is correct by substituting x = 4 in the two sides of the original equation to verify that when x = 4 the two sides are equal.

Left side: 4x - 5 = 4 × 4 - 5 = 16 - 5 = 11

Right side: 7 + x = 7 + 4 = 11.

Thus x = 4 is the correct answer.

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.