4x-8≤12

Answer 1

To solve the inequality \( 4x - 8 \leq 12 \), follow these steps:

1. Add 8 to both sides: \[ 4x - 8 + 8 \leq 12 + 8 \] This simplifies to: \[ 4x \leq 20 \]

2. Divide both sides by 4: \[ \frac{4x}{4} \leq \frac{20}{4} \] This simplifies to: \[ x \leq 5 \]

So, the solution to the inequality is: \[ x \leq 5 \]

In interval notation, this can be expressed as: \[ (-\infty, 5] \]

Answer 2

solve the equation and write the answer using set notation
14/x-2 = 7 and x ≠ 2

Answer 3

To solve the equation

\[ \frac{14}{x} - 2 = 7, \]

follow these steps:

1. Isolate the term with \(x\): Add 2 to both sides of the equation: \[ \frac{14}{x} = 7 + 2 \] This simplifies to: \[ \frac{14}{x} = 9. \]

2. Multiply both sides by \(x\) (note that \(x \neq 0\) to avoid division by zero): \[ 14 = 9x. \]

3. Solve for \(x\): Divide both sides by 9: \[ x = \frac{14}{9}. \]

Since the problem states that \(x \neq 2\), we check if our solution \(\frac{14}{9}\) is equal to 2. Since \(\frac{14}{9} \approx 1.56\), which is not equal to 2, it satisfies the \(x \neq 2\) condition.

Thus, the solution to the equation is

\[ \left{ \frac{14}{9} \right}. \]

Using set notation, the final answer is: \[ { \frac{14}{9} }. \]

Answer 4

rearrange to highlight h
A=b*h

Answer 5

To rearrange the equation \( A = b \cdot h \) to highlight \( h \), follow these steps:

1. Isolate \( h \): Divide both sides of the equation by \( b \) (assuming \( b \neq 0 \)): \[ h = \frac{A}{b}. \]

Now, the equation is rearranged to highlight \( h \): \[ h = \frac{A}{b}. \]