Math / Algebra

QuestionPractice and Problem-Solving Exercises Mathematical PRACTICES
Solve each equation. Check your answer.
10. $5 x-1=x+15$
11. $4 p+2=3 p-7$
12. $6 m-2=2 m+6$
13. $3+5 q=9+4 q$
14. $8-2 y=3 y-2$
15. $3 n-5=7 n+11$
16. $2 b+4=-18-9 b$
17. $-3 c-12=-5+c$
18. $-n-24=5-n$

Studdy Solution

STEP 1

What is this asking? We're solving for $x$ in the equation $5x - 1 = x + 15$ , meaning we need to find the value of $x$ that makes both sides equal! Watch out! Don't forget to double-check your answer by plugging it back into the original equation.
It's a super simple way to make sure you aced it!

STEP 2

1. Isolate the Variable Term
2. Isolate the Variable
3. Verify the Solution

STEP 3

Let's start with our equation: $5x - 1 = x + 15$ Our goal is to get all the $x$ terms on one side and all the constant terms on the other.

STEP 4

Let's move the $x$ term from the right side to the left side.
To do this, we'll subtract $x$ from both sides of the equation.
Remember, whatever we do to one side, we must do to the other to keep the equation balanced! $5x - 1 - x = x + 15 - x$ This simplifies to: $4x - 1 = 15$ We've successfully moved all the $x$ terms to the left side!

STEP 5

Now, let's move that constant term, $-1$ , from the left side to the right side.
We'll do this by adding $1$ to both sides of the equation: $4x - 1 + 1 = 15 + 1$ This simplifies to: $4x = 16$

STEP 6

We're almost there!
Now, we just need to isolate $x$ .
Since $x$ is being multiplied by $4$ , we'll divide both sides by $4$ to get $x$ by itself: $\frac{4x}{4} = \frac{16}{4}$ This gives us our solution: $x = 4$

STEP 7

Let's double-check our work by substituting our solution, $x = 4$ , back into the original equation: $5x - 1 = x + 15$ Substituting $x = 4$ , we get: $5 \cdot 4 - 1 = 4 + 15$

STEP 8

Simplifying both sides, we have: $20 - 1 = 19$ $19 = 19$ Since both sides are equal, our solution $x = 4$ is correct!

STEP 9

$x = 4$

Was this helpful?

QuestionPractice and Problem-Solving Exercises Mathematical PRACTICES
Solve each equation. Check your answer.
10. $5 x-1=x+15$
11. $4 p+2=3 p-7$
12. $6 m-2=2 m+6$
13. $3+5 q=9+4 q$
14. $8-2 y=3 y-2$
15. $3 n-5=7 n+11$
16. $2 b+4=-18-9 b$
17. $-3 c-12=-5+c$
18. $-n-24=5-n$

Studdy Solution

STEP 1

What is this asking? We're solving for $x$ in the equation $5x - 1 = x + 15$ , meaning we need to find the value of $x$ that makes both sides equal! Watch out! Don't forget to double-check your answer by plugging it back into the original equation.
It's a super simple way to make sure you aced it!

STEP 2

1. Isolate the Variable Term
2. Isolate the Variable
3. Verify the Solution

STEP 3

Let's start with our equation: $5x - 1 = x + 15$ Our goal is to get all the $x$ terms on one side and all the constant terms on the other.

STEP 4

STEP 5

Now, let's move that constant term, $-1$ , from the left side to the right side.
We'll do this by adding $1$ to both sides of the equation: $4x - 1 + 1 = 15 + 1$ This simplifies to: $4x = 16$

STEP 6

We're almost there!
Now, we just need to isolate $x$ .
Since $x$ is being multiplied by $4$ , we'll divide both sides by $4$ to get $x$ by itself: $\frac{4x}{4} = \frac{16}{4}$ This gives us our solution: $x = 4$

STEP 7

Let's double-check our work by substituting our solution, $x = 4$ , back into the original equation: $5x - 1 = x + 15$ Substituting $x = 4$ , we get: $5 \cdot 4 - 1 = 4 + 15$

STEP 8

Simplifying both sides, we have: $20 - 1 = 19$ $19 = 19$ Since both sides are equal, our solution $x = 4$ is correct!

STEP 9

$x = 4$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

STEP 2

1. Isolate the Variable Term2. Isolate the Variable3. Verify the Solution

STEP 3

Let's **start** with our equation: 5x−1=x+155x - 1 = x + 155x−1=x+15 Our goal is to get all the xxx terms on one side and all the constant terms on the other.

STEP 4

STEP 5

Now, let's move that constant term, −1-1−1, from the left side to the right side.We'll do this by adding 111 to both sides of the equation: 4x−1+1=15+14x - 1 + 1 = 15 + 14x−1+1=15+1 This simplifies to: 4x=164x = 164x=16

STEP 6

We're almost there!Now, we just need to isolate xxx.Since xxx is being multiplied by 444, we'll divide both sides by 444 to get xxx by itself: 4x4=164\frac{4x}{4} = \frac{16}{4}44x​=416​ This gives us our **solution**: x=4x = 4x=4

STEP 7

Let's **double-check** our work by substituting our solution, x=4x = 4x=4, back into the original equation: 5x−1=x+155x - 1 = x + 155x−1=x+15 Substituting x=4x = 4x=4, we get: 5⋅4−1=4+155 \cdot 4 - 1 = 4 + 155⋅4−1=4+15

STEP 8

Simplifying both sides, we have: 20−1=1920 - 1 = 1920−1=19 19=1919 = 1919=19Since both sides are equal, our solution x=4x = 4x=4 is **correct**!

STEP 9

x=4x = 4x=4

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Isolate the Variable Term
2. Isolate the Variable
3. Verify the Solution

Let's start with our equation: $5x - 1 = x + 15$ Our goal is to get all the $x$ terms on one side and all the constant terms on the other.

Now, let's move that constant term, $-1$ , from the left side to the right side.
We'll do this by adding $1$ to both sides of the equation: $4x - 1 + 1 = 15 + 1$ This simplifies to: $4x = 16$

We're almost there!
Now, we just need to isolate $x$ .
Since $x$ is being multiplied by $4$ , we'll divide both sides by $4$ to get $x$ by itself: $\frac{4x}{4} = \frac{16}{4}$ This gives us our solution: $x = 4$

Let's double-check our work by substituting our solution, $x = 4$ , back into the original equation: $5x - 1 = x + 15$ Substituting $x = 4$ , we get: $5 \cdot 4 - 1 = 4 + 15$

Simplifying both sides, we have: $20 - 1 = 19$ $19 = 19$ Since both sides are equal, our solution $x = 4$ is correct!

$x = 4$