Question 154026
Ok, let's look at the first one:
{{{x+6 = 3(5-x)}}} The first thing you want to do is to apply the distributive property to the right side.
{{{x+6 = 3*5-3*x}}} Simplify this.
{{{x+6 = 15-3x}}} Now subtract x from both sides to get the variable, x, on on side of the equation, and it really doesn't matter which side but here, it ends up on the right side.
{{{x-x+6 = 15-3x-x}}} Simplify.
{{{6 = 15-4x}}} Now that you have the x on one side, you subtract 15 from both sides to leave the x-term by itself on the right side.
{{{6-15 = -4x+15-15}}} Simplify.
{{{-9 = -4x}}} Now you need to "undo" the multiplication of the x by (-4), so you would divide both sides by (-4).
{{{-9/(-4) = -4x/(-4)}}} Simplify.
{{{9/4 = x}}} or {{{highlight(x = 9/4)}}}
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{{{(3/2)x+1 = 13}}} This problem is easier to handle if you can "clear" the fraction and you can do this by multiplying through by the denominator of 2.
{{{2((3/2)x+1) = 2(13)}}}
{{{2*(3/2)x+2*1 = 2*13}}} Simplifying this, you'll get:
{{{3x+2 = 26}}} Now, to isolate the x-term. you'll subtract 2 from both sides of the equation.
{{{3x+2-2 = 26-2}}} Simplify.
{{{3x = 24}}} Finally, divide both sides by 3 to get the x by itself.
{{{3x/3 = 24/3}}} Simplify.
{{{highlight(x = 8)}}}