Question

question 5
what is the solution to the equation 4(x - 3) = 20?
○ x = 3
○ x = 8
○ x = 5
○ x = 6
question 6
evaluate the expression (2² × 2⁻⁴) ÷ 2⁻¹

Explanation:

QUESTION 5

Step1: Divide both sides by 4

To isolate the term with \(x\), we divide both sides of the equation \(4(x - 3)=20\) by 4.
\[
\frac{4(x - 3)}{4}=\frac{20}{4}
\]
Simplifying both sides, we get \(x - 3 = 5\).

Step2: Add 3 to both sides

To solve for \(x\), we add 3 to both sides of the equation \(x - 3 = 5\).
\[
x-3 + 3=5 + 3
\]
Simplifying both sides, we find that \(x = 8\).

Step1: Use exponent rule \(a^m\times a^n=a^{m + n}\)

First, simplify the numerator \(2^2\times2^{-4}\) using the rule of exponents for multiplication. For \(a = 2\), \(m = 2\), and \(n=- 4\), we have:
\[
2^2\times2^{-4}=2^{2+( - 4)}=2^{-2}
\]
So the expression becomes \(\frac{2^{-2}}{2^{-1}}\).

Step2: Use exponent rule \(\frac{a^m}{a^n}=a^{m - n}\)

Now, simplify \(\frac{2^{-2}}{2^{-1}}\) using the rule of exponents for division. For \(a = 2\), \(m=-2\), and \(n = - 1\), we get:
\[
\frac{2^{-2}}{2^{-1}}=2^{-2-( - 1)}=2^{-1}
\]

Step3: Simplify \(2^{-1}\)

Recall that \(a^{-n}=\frac{1}{a^n}\), so \(2^{-1}=\frac{1}{2}\).

Answer:

\(x = 8\) (corresponding to the option with \(x = 8\))

QUESTION 6