Math 017 Materials With Exercises

■ Solve the following equation2x 9 34x.2x 9 34xIf x' s appear on both sides, „bring all x' s on one side‟. 4 xis subtracted, thus we need to add (opposite operation) 4 xto both sides.2x 9 4x 34x 4xCollect like terms (on both sides separately!)6x 9 3Now, the equation is in the form we already know how tosolve. We will continue solving it using methods introducedearlier. To isolate x , we first „bring 9 to the other side‟ byadding it to both sides.6x 9 9 39Simplify.6x 12Divide both sides by 6.6x12 Simplify.6 6x 2The solution of 2x 9 34xis x 2 ■■ Solve the following equation 3(x 2) 9.3(x 2) 9If parentheses are involved on one or both sides of theequation, we first remove parentheses by applying theDistributive Law.3x 6 9The equation is in the form we already know how tosolve: add 6 to both sides. The operation of adding 6 to 6 can easily be performed mentally, without recordingit and this is how we will be doing it from now on. Youare encouraged to do the same.3x 15Divide each side by 3.15x Simplify.3x 5The solution of 3(x 2) 9 is x 5. ■Example 8.3 Solve the following equations.a) 98 xb) 4 x 5 15 xSolution:a) x 98 To eliminate the minus sign, multiply (or equivalentlydivide) both sides by 1 (recall that x 1 x ).1(x ) 1(98)Perform the indicated operations.x 98The solution of x 98 is x 98.b) 4 x 5 15 x „Bring all x‟s on one side‟ by subtracting x from both81