Question

write an algebraic equation for the sentence. then solve the equation.

1. the difference of a number and fifteen is negative fifteen.
2. twenty-six is the sum of a number and forty.
3. seven eighths is the difference of a number and one fourth.

Explanation:

Problem 24:

Step1: Define variable & set equation

Let the number be $x$. The difference of $x$ and 15 is $x - 15$, which equals $-15$.
$x - 15 = -15$

Step2: Solve for $x$

Add 15 to both sides.
$x - 15 + 15 = -15 + 15$
$x = 0$

Problem 25:

Step1: Define variable & set equation

Let the number be $x$. The sum of $x$ and 40 is $x + 40$, which equals 26.
$x + 40 = 26$

Step2: Solve for $x$

Subtract 40 from both sides.
$x + 40 - 40 = 26 - 40$
$x = -14$

Problem 26:

Step1: Define variable & set equation

Let the number be $x$. The difference of $x$ and $\frac{1}{4}$ is $x - \frac{1}{4}$, which equals $\frac{7}{8}$.
$x - \frac{1}{4} = \frac{7}{8}$

Step2: Solve for $x$

Add $\frac{1}{4}$ (or $\frac{2}{8}$) to both sides.
$x - \frac{1}{4} + \frac{1}{4} = \frac{7}{8} + \frac{2}{8}$
$x = \frac{9}{8}$

Answer:

1. Equation: $x - 15 = -15$; Solution: $x = 0$
2. Equation: $x + 40 = 26$; Solution: $x = -14$
3. Equation: $x - \frac{1}{4} = \frac{7}{8}$; Solution: $x = \frac{9}{8}$