Solve the following equations: a. 7x−63+2=6 b. 2x−3=x−3

Question

Aniqa O&#039;Neill · Accepted Answer

Step 1
When there is an equality sign between two expressions, the powers or exponents on both sides are equal. For solving the values for expressions, the exponents are made equal on both sides. Thus, it helps in solving an unknown value of variable in an equation.
Quadratic equations are those in which the highest power of the equation is 2, and it has two roots.
Step 2
(a) To calculate the value of x, subtract 2 from both sides of the equation and then take cube on each side of the equation.
Separate the x term. Then, the value of x is obtained.
$\sqrt[3]{7 x - 6} + 2 = 6$
$\sqrt[3]{7 x - 6} = 6 - 2$
$\sqrt[3]{7 x - 6} = 4$
$7 x - 6 = 64$
$7 x = 70$
$x = 10$
Hence, the value of x is 10.
Step 3
(b) To simplify, first take square on each side of equation to remove the square root.
Use the algebraic identity ${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$ .
$\sqrt{2 x - 3} = x - 3$
$2 x - 3 = x^{2} - 6 x + 9$
$x^{2} - 6 x + 9 - 2 x + 3 = 0$
$x^{2} - 8 x + 12 = 0$
$(x - 6) (x - 2) = 0$
Now, the value of x is obtained as below:
$x - 6 = 0$
$x = 6$
$x - 2 = 0$
$x = 2$
Discarding $x = 2$ as it doesn't satisfy the equation $\sqrt{2 x - 3} = x - 3$
Hence, the values of x is 6.

Solve the following equations:a. \sqrt[3]{7x-6}+2=6

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