If these have a solution, they are all solved the same way.
.. Eliminate parentheses using the distributive property.
.. Collect terms.
.. If variables are on both sides of the equation, identify the variable term with the smallest or most-negative coefficient. Add the opposite of that term to the equation. (If the same variable term exists on both sides of the equation, it doesn't matter which one you pick.)
.. If a constant is on the same side of the equation as the remaining variable term, add the opposite of that constant. (If no variable terms remain, you can determine if the equation is true or false at this point. True: every value of the variable is a solution; False: no value of the variable is a solution.)
.. Divide by the coefficient of the variable, if there is a variable term.
Whenever you add, subtract, multiply, or divide one side of the equation by a number, you must do the same to the other side. (Keep the equal sign true.)
1) 154 = -4(8 +6r) +24r
.. 154 = -32 -24r +24r
.. 154 = -32 . . . . . . . . . . . . false, no solution
2) -28 = -7(3x +4) +21x
.. -28 = -21x -28 +21x
.. -28 = -28 . . . . . . . . . . . . true, for x ∈ ℝ . . . . any real number x
3) -(-4x +7) = -2 +4x
.. 4x -7 = -2 +4x
.. -7 = -2 . . . . . . . . . . . . . . false, no solution
4) no solution
5) no solution
6) true for any real number k.
