Question

In the following exercises, translate to an algebraic expression and simplify if possible.

The sum of 3 and $-15$, increased by 7.

Short answer

The given statement can be translated as $\left[3+\left(-15\right)\right]+7$and the simplified value is $-5$.

Step-by-step solution

Step 1. Concept Used. 

The phrase "The sum of $a$and $b$" and "$a$ increased by $b$" indicates the operation of addition and rewritten as $a+b$.

Step 2. Write the given statement using mathematical notations.

The sum of 3 and $-15$be written as

$3+\left(-15\right)$

Then, it is given that the sum of 3 and $-15$, that is, $3+\left(-15\right)$is increased by 7. Write it as a mathematical expression.

$\left[3+\left(-15\right)\right]+7$

Step 3. Simplify. 

Start with the grouping symbol. Rewrite $3+\left(-15\right)$by using the subtraction property $a+\left(-b\right)=a-b$.$a+\left(-b\right)=a-b$.

Subtract 15 from 3 inside the brackets.

$\begin{array}{rcl}\left[3+\left(-15\right)\right]+7& =& \left[3-15\right]+7\\ & =& -12+7\end{array}$

Step 4. Perform Addition. 

Add $-12$and 7 in the obtained expression.

$-12+7=-5$

Step 5. Conclusion. 

The given statement can be translated as $\left[3+\left(-15\right)\right]+7$and the simplified value is $-5$.