Solve the equation algebraically. Verify your results using a graphing utility. (13)x=2−(23)x

Question

Solve the equation algebraically. Verify your results using a graphing utility.   (13)x=2−(23)x

Annie Gonzalez · Accepted Answer

Step 1  The given equation is,  13x=2−23x  We need to solve the given equation for x  Step 2  On solving the given equation, we get  13x=2−23x  13x+23x=2  (13+23)x=2  (1+23)x=2  (33)x=2  x=2  Therefore, the solution of the given equation is 2.

vrangett · Accepted Answer

13x=2−(23)x  1x3=2−(23)x  x3=2−(23)x  x3=2−1⋅23x  x3=2−23x  x3=2+−2x3  x3=3⋅23+−2x3  x3=3⋅2−2x3  x3=6−2x3  x3=−2x+63  3⋅x3=3(−2x+63)  x=−2x+6  x+2x=−2x+6+2x  3x=6  3x3=63  x=2

nick1337 · Accepted Answer

1) convert the product of monomials to a fraction 13x=2−(23)x 1x3=2−(23)x 2) Multiply by 1 x3=2−(23)x 3) Multiply numbers x3=2−1⋅23x x3=2−23x 4) Convert the product of monomials to a fraction x3=2+−2x3 5) Bring to a common denominator x3=3⋅23+−2x3 6) Add fractions with the same denominator x3=3⋅2−2x3 7) Multiply numbers x3=6−2x3 8) Rearrange the terms of the equation x3=−2x+63 9) To eliminate the denominators, multiply all terms of the equation by the same number 3⋅x3=3(−2x+63) 10) Reduce the denominator x=−2x+6 11) Add 2x to both sides of the equation x+2x=−2x+6+2x 12) Simplify 3x=6 13) Divide both sides of the equation by the same term 3x3=63 14) Simplify x=2

Solve the equation algebraically. Verify your results using a graphing

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