What is the sum of the expressions (2/3x −7)+(1/3 x+5)?
1 answer:
The answer is Final result : x - 2 Step by step solution : Step 1 : 1 Simplify — 3 Equation at the end of step 1 : 2 1 ((—•x)-7)+((—•x)+5) 3 3 Step 2 : Rewriting the whole as an Equivalent Fraction : 2.1 Adding a whole to a fraction Rewrite the whole as a fraction using 3 as the denominator : 5 5 • 3 5 = — = ————— 1 3 Equivalent fraction : The fraction thus generated looks different but has the same value as the whole Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator Adding fractions that have a common denominator : 2.2 Adding up the two equivalent fractions Add the two equivalent fractions which now have a common denominator Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible: x + 5 • 3 x + 15 ————————— = —————— 3 3 Equation at the end of step 2 : 2 (x + 15) ((— • x) - 7) + ———————— 3 3 Step 3 : 2 Simplify — 3 Equation at the end of step 3 : 2 (x + 15) ((— • x) - 7) + ———————— 3 3 Step 4 : Rewriting the whole as an Equivalent Fraction : 4.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using 3 as the denominator : 7 7 • 3 7 = — = ————— 1 3 Adding fractions that have a common denominator : 4.2 Adding up the two equivalent fractions 2x - (7 • 3) 2x - 21 ———————————— = ——————— 3 3 Equation at the end of step 4 : (2x - 21) (x + 15) ————————— + ———————— 3 3 Step 5 : Adding fractions which have a common denominator : 5.1 Adding fractions which have a common denominator Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible: (2x-21) + (x+15) 3x - 6 ———————————————— = —————— 3 3 Step 6 : Pulling out like terms : 6.1 Pull out like factors : 3x - 6 = 3 • (x - 2) Final result : x - 2 100% Verified! Hope This Helps! :)
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