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What is the solution to this equation?

[tex]\[ 7 = \sqrt[3]{2-x} = 12 \][/tex]

The solution is [tex]\( x = \square \)[/tex]


Sagot :

To solve the equation [tex]\(7 = \sqrt[3]{2 - x} = 12\)[/tex], let's follow a logical step-by-step approach:

1. Isolate the cube root term:

We can rewrite the equation focusing on isolating the cube root:
[tex]\[ 7 = \sqrt[3]{2 - x} \][/tex]
This implies:
[tex]\[ \sqrt[3]{2 - x} = 12 - 7 \][/tex]
Simplifying the right side of the equation:
[tex]\[ \sqrt[3]{2 - x} = 5 \][/tex]

2. Eliminate the cube root by cubing both sides of the equation:

To remove the cube root, we cube both sides:
[tex]\[ \left(\sqrt[3]{2 - x}\right)^3 = 5^3 \][/tex]
This simplifies to:
[tex]\[ 2 - x = 125 \][/tex]

3. Solve for [tex]\(x\)[/tex]:

We need to isolate [tex]\(x\)[/tex] by rearranging the equation:
[tex]\[ 2 - 125 = x \][/tex]
Simplifying the left side:
[tex]\[ -123 = x \][/tex]

Therefore, the solution to the equation is:
[tex]\[ x = -123 \][/tex]