Algebraic expressions

Question

3 times the sum of 5 and x

Answer 1

= 3(5+x)

= 15 +3x

= 3 times the sum of 5 and x

Answer 2

When writing out this equation, remember the rules of PEMDAS; where in order for computing numbers go as follow:

1. P - Parentheses; ex. 3 + (5 * x) - you first multiply what is in the parentheses; so it will be 3 + 5x
2. E - Exponent; ex. cont. 3 + (5^2 * x) - in this example, you calculate 5^2 BEFORE multiplying by x; so it will be 3 + (25 * x) or 3 + 25x
3. M - Multiply ex. cont. 3 + (5^2 * 3 * x) - in this example, we first do 5^2 THEN begin multiplying left to right in the parentheses; so it will be 3 + (25 * 3 * x) then 3 + (75 * x), finally 3 + 75x
4. D - Divide ex. cont. 3 + (5^2 * 3 * x / 5) - in this example, we first do 5^2 THEN from left to right, multiply or divide based on what comes next, let's take it to 3 + (25 * 3 * x / 5) then we have 3 + (75 * x / 5), which will be 3 + (75x / 5) which will finally be 3 + 15x
5. A - Addition ex. cont. 3 + (5 + 3 + 5^2 * 3 * x / 5) - in this example, we first do 5^2 THEN multiply and divide in order...this will simplify to 3 + (8 + 15x) OR 11 + 15x.
6. S - Subtraction ex. cont. 3 + (5 - 2 + 3 + 5^2 * 3 * x / 5) in this example, we first do 5^2 THEN multiply and divide in order...this will simplify to 3 + (5 - 2 + 3 + 15x). Just like multiply and divide, we go from left to right with either addition or subtraction, whatever comes first! So, simplifying the above will be 3 + (3 + 3 + 15x) = 3 + (6 + 15x) = 9 + 15x

So, writing the requested question of 3 times the sum of 5 and x we can write it out as 3 * (5 + x) because the keyword sum in the proposed question says that we take the sum of 5 and x FIRST and what we defined in PEMDAS, we can put that in parentheses so the written out equation is 3 * (5 + x) OR 3(5 + x)

Note: A number OR variable next to a parentheses is the same idea as having a * or multiplication symbol between a number OR variable next to a parentheses

Answer 3

"The sum of 5 and x" can be written as 5+x. However, you want to surround this expression with parentheses.

Then multiplying this entire expression by 3 gives: 3(5+x).

This is a good opportunity to review your order of operations. PEMDAS. Because "addition/sum" falls below multiplication in the order of operations, parentheses must be used, so that the parentheses puts the "sum" expression 5+ x above the multiplication by 3.

If not, and you simply wrote 3*5+x, then this expression results in 15+x, which is incorrect!