How do you set up and solve a word problem like “twice a number plus 5 is 17”?

Question

Algebra word problems can feel confusing because it’s hard to know where to start. What’s the best way to turn a sentence like “twice a number plus 5 is 17” into an equation and solve it?

Answer 1

How do you set up and solve a word problem like “twice a number plus 5 is 17”?

First of all this is a two part question. First you are asking how to set up the problem. This is done by translating English into an Algebraic Equation (meaning there is at least one unknown, i.e., or variable, in the equation). Then lastly, you are asking how to solve the Algebraic Equation? This is done by performing inverse operations to both sides of the Algebraic Equation.

The part of the question above that needs to translate from English into an Algebraic Equation is:

“twice a number plus 5 is 17“. Then to solve the Algebraic Equation you need to calculate what the number is that makes this statement true by using the appropriate inverse mathematical operations.

To translate, “twice a number plus 5 is 17“ into an algebraic equation, use the following rules, which are not necessarily collectively exhaustive:

“+” : plus, more than, the sum of, the total of, add, increased by;

”-“ : minus, less than, decreased, the difference of;

”x” : times, product, twice (2 times), multiplied by;

”/“ : quotient, divided, ratio; and

“=“ : is, equals

Using these rules, I can start translating the above phrase, into mathematical operations. So “Twice” is translated into mathematics as 2 times. “A number” is the unknown that makes this equation an Algebraic Equation. We use English letters in algebra to represent an unknown value. These letters are most often, x, y, z, a, b, c, m, or n. I’ll choose the most popular of theee Algebraic letters, “x”. “Plus” means to +. “Is” means =.

So combining the phrase and the rules above I get the following Algebraic Equation:

2x + 5 = 17. This is the answer to the first part of the question, how do you set up a word problem.

Now to solve an algebraic equation with one variable, I need to use reverse operations to get all the constant values on one side of the equation and the unknown (variable) alone on the other side of the equation. Then after combining the constants, that value becomes the value for the unknown, and the word problem is solved.

So to solve this Algebraic Equation, 2x + 5 = 17,

first perform the reverse operation of +5, which is -5, to both sides of the equation. Five is subtracted from both sides of the equation in order to keep the equation balanced. This gives: 2x + 5 - 5 = 17 - 5.

Combining the constants to simplify the equation, we get 2x = 12. Now 2 is also a constant and it is connected to the unknown x by multiplication. The inverse of multiplication is division. So now divide both sides of the equation by 2. We get:

2x/ 2 = 12/2

Then simplifying we get X = 6. Now that completes the second part of the question of how to solve the word problem.

We can check this answer by substituting 6 for the unknown (or variable “x”) in the original equation to see if we get the answer 17. If so, we would have done this step correctly.

2(6) + 5 =17

12 + 5 = 17

17 = 17

Problem solved correctly.

Answer 2

The goal is to identify which words translate to which mathematical symbols.

“twice a number plus 5 is 17”

Let x = "a number".

When the question prompts you to use "twice a number" that translates to 2x, or twice that number. Next, the question says "plus 5". This means that we're now adding 5 to the quantity of 2x.

Lastly, the question says "is 17". The word "is" directly translates to the equal sign (=) in these types of problems.

So the final equation is 2x+5 = 17. Now, you must isolate x and solve for it, resulting in the answer of x=6.

Answer 3

Algebra word problems can feel confusing, but if you break it down, you'll have an easier time deciphering the word problem!

Twice a number plus 5 is 17

1. Twice means two times, or: 2x
2. Let's say a number is the variable X
3. Plus means +, or adding
4. Is means equals to, or =

So, putting it all together:

twice a number means 2X

2X plus 5 means 2X + 5

2X + 5 is 17 means 2X + 5 = 17

We are left with 2X + 5 = 17. Let's get our variable X alone and on one side. To do that, we need to subtract 5 on both sides, leaving us with:

2X + 5 - 5 = 17 - 5

2X = 12

Now, we need to divide both sides by 2 to get:

2X / 2 = 12 / 2

X = 6

And there you have it, your answer is 6!

My tip for you would be to break down the word problem and convert the words into math.

Good luck!

Answer 4

2x + 5= 17

2x = 12

x = 6

that's the answer you likely want

but it could be

2(x+5) = 17

2x+10 = 17

2x = 7

x = 7/2 = 3 1/2 = 3.5

English doesn't translate unambiguously into precise mathematics

the context helps sort out any ambiguities

Answer 5

This kind of problem is all about translating words into math.

Let’s break it down:

1. “Twice a number” → 2x
2. “plus 5” → +5
3. “is 17” → = 17

So the equation becomes:

2x + 5 = 17

Now solve it:

1. Subtract 5 from both sides:
2. 2x = 12
3. Divide both sides by 2:
4. x = 6

✅ Final Answer: x = 6

🧠 Tip: Underline the key parts of the word problem and turn them into math one phrase at a time. That makes it way easier to decode!