Question

which of the following is not and equation? a) $y = 6x - 4$ b) $55 = 6 + d^2$ c) $(4 \cdot 3b) + (8 \div 2c)$ if $f(x) = -4x + 7$ find $f(2)$ find $f(-3)+1$

Explanation:

First Question: Which of the following is NOT an equation?

An equation is a mathematical statement that shows the equality of two expressions, meaning it has an "=" sign. Let's analyze each option:

• Option A: \( y = 6x - 4 \) has an "=" sign, so it is an equation.
• Option B: \( 55 = 6 + d^2 \) has an "=" sign, so it is an equation.
• Option C: \( (4 \cdot 3b) + (8 \div 2c) \) is just an expression with operations (multiplication, division, addition) but no "=" sign to show equality, so it is not an equation.

Step 1: Substitute \( x = 2 \) into \( f(x) \)

To find \( f(2) \), we replace \( x \) in the function \( f(x) = -4x + 7 \) with 2. So we get \( f(2)=-4(2)+7 \).

Step 2: Calculate the value

First, calculate \( -4(2)=-8 \). Then, add 7: \( -8 + 7=-1 \).

Step 1: Substitute \( x = -3 \) into \( f(x) \)

To find \( f(-3) \), we replace \( x \) in the function \( f(x) = -4x + 7 \) with -3. So we get \( f(-3)=-4(-3)+7 \).

Step 2: Calculate \( f(-3) \)

First, calculate \( -4(-3)=12 \). Then, add 7: \( 12 + 7 = 19 \).

Step 3: Add 1 to \( f(-3) \)

Now, we need to find \( f(-3)+1 \), so we add 1 to the result of \( f(-3) \): \( 19 + 1 = 20 \).

Answer:

C. \( (4 \cdot 3b) + (8 \div 2c) \)

Second Question: If \( f(x) = -4x + 7 \), find \( f(2) \)