66Divide both sides by6x=3Our SolutionA second type of problem that becomes a two-step equation after a bit of work isone where we see the variable on both sides.This is shown in the followingexample.Example 61.4x−6=2x+10Notice here thexis on both the left and right sides of the equation. This canmake it difficult to decide which side to work with. We fix this by moving one ofthe terms withxto the other side, much like we moved a constant term. Itdoesn’t matter which term gets moved,4xor2x,however, it would be theauthor’s suggestion to move the smaller term (to avoid negative coefficients). Forthis reason we begin this problem by clearing the positive2xby subtracting2xfrom both sides.4x−6=2x+10Notice the variable on both sides−2x−2xSubtract2xfrom both sides2x−6=10Focus on the subtraction first+6 +6Add6to both sides2x=16Focus on the multiplication by222Divide both sides by2x=8Our Solution!The previous example shows the check on this solution.Here the solution isplugged into thexon both the left and right sides before simplifying.Example 62.4(8)−6=2(8)+10Multiply4(8)and2(8)first32−6=16+10Add and Subtract26=26True!The next example illustrates the same process with negative coefficients. Noticefirst the smaller term with the variable is moved to the other side, this time byadding because the coefficient is negative.