Use the properties of equality to solve the following linear equations by moving all terms with the unknown variable to the left, all other terms to the right, and then simplifying:

With the equation reduced to 0 = 0, the equation is an identity. An identity is an equation in which any real number can be substituted for x and the equation will remain valid.

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(a) 3x+8=5x-6 3x+8=5x-6 3x-5x=-6-8 -2x=-14 x=7 (c) 6(4x+5)-3x=19-2(7x+82) 6(4x+5)-3x=19-2(7x+82) 24x+30-3x=19-14x-164 24x 3x+14x19-164-30 - 35x=-175 x=-5 (b) 32-3x= 9x-40 32 3x9x-40 -3x-9x=-40-32 -12x=-72 x=6 (d) 6x 13 = 3(2x-11) +20 - 6x 13 3(2x-11)+20 6x-13=6x-33 +20 6x-6x=-33 +20+13 0=0