Solve the equation and check the solution. (z)/(6)+2=8 Solve the equation 7+(10)

Question

Solve the equation and check the solution. (z)/(6)+2=8 Solve the equation 7+(10)/(x)=x+4 Solve the equation (a-5)/(3)+(a-6)/(4)=(7)/(3) Solve the equation (2y)/(y-10)+1=(8y)/(y-10) Solve the equation and check the proposed solution. 5+(12)/(a-3)=(4a)/(a-3) Solve the equation and check the solution. (z)/(6)+2=8 Solve the equation 7+(10)/(x)=x+4 Solve the equation (a-5)/(3)+(a-6)/(4)=(7)/(3) Solve the equation (2y)/(y-10)+1=(8y)/(y-10) Solve the equation and check the proposed solution. 5+(12)/(a-3)=(4a)/(a-3)

Explanation / Answer

1. z/6 + 2 = 8 First subtract 2 from each side z/6 = 6 Mult. each side by 6 z = 36 (Ans) 2. 7 + 10/x = x+4 First subtract 7 from each side 10/x = x-3 Mult. each side by x 10 = x2-3x Subtract 10 from each side 0 = x2-3x-10 Solve the quadratic using foil or quadratic equation (x-5)(x+2)=0 Therefore x = 5, -2 (Ans) 3. (a-5)/3 + (a-6)/4 = 7/3 Use LCM of 12 OR just multiply each side by 12 4(a-5) + 3(a-6) = 28
Expand brackets 4a-20+3a-18 = 28 7a-38 = 28 7a = 66 a = 66/7 (Ans) 4.(2y)/(y-10)+1=(8y)/(y-10) Subtract 8y/(y-10) from each side 2y/(y-10) + 1 - 8y/(y-10) = 0 Use LCM of y-10 OR multiply each side by y-10 2y + y-10-8y = 0 -5y-10=0 y = -2 (Ans) 5. 5+(12)/(a-3)=(4a)/(a-3) Subtract 12/(a-3) from each side 5 = 4a/(a-3) - 12/(a-3) The RHS has the same denominator so subtract 5 = (4a-12)/(a-3) Multiply each side by a-3 5(a-3) = 4a-12 5a-15 = 4a-12 a = -12+15 a = 3 (Ans)
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