Math / Algebra

QuestionScore: 30/190 Answered: 3/19 Question 8
The following inequality has a solution in the form $x>A$ . Solve the inequality and place the correct value of $A$ into the box. $14 x-13>-5+3 x$
Answer: $x>$ $\square$ Enter your answer as an integer or a reduced fraction in the form A/B.

Studdy Solution

STEP 1

What is this asking? We need to find the smallest value of $x$ that makes the inequality $14x - 13 > -5 + 3x$ true. Watch out! Remember to flip the inequality sign if you multiply or divide both sides by a negative number!
But we won't need to do that here.

STEP 2

1. Isolate the $x$ terms.
2. Isolate $x$ .

STEP 3

First, let's get all the $x$ terms on one side.
We can do this by subtracting $3x$ from both sides of the inequality: $14x - 13 - 3x > -5 + 3x - 3x$ $11x - 13 > -5$ Why did we do that?
Because it helps us get closer to having $x$ all by itself!

STEP 4

Now, let's get rid of that $-13$ on the left side.
We can do this by adding $13$ to both sides: $11x - 13 + 13 > -5 + 13$ $11x > 8$ Awesome! We're almost there.

STEP 5

To finally isolate $x$ , we need to divide both sides of the inequality by $11$ : $\frac{11x}{11} > \frac{8}{11}$ $x > \frac{8}{11}$ And there we have it!

STEP 6

The solution to the inequality is $x > \frac{8}{11}$ .
So, the value of $A$ is $\frac{8}{11}$ .

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QuestionScore: 30/190 Answered: 3/19 Question 8
The following inequality has a solution in the form $x>A$ . Solve the inequality and place the correct value of $A$ into the box. $14 x-13>-5+3 x$
Answer: $x>$ $\square$ Enter your answer as an integer or a reduced fraction in the form A/B.

Studdy Solution

STEP 1

What is this asking? We need to find the smallest value of $x$ that makes the inequality $14x - 13 > -5 + 3x$ true. Watch out! Remember to flip the inequality sign if you multiply or divide both sides by a negative number!
But we won't need to do that here.

STEP 2

1. Isolate the $x$ terms.
2. Isolate $x$ .

STEP 3

First, let's get all the $x$ terms on one side.
We can do this by subtracting $3x$ from both sides of the inequality: $14x - 13 - 3x > -5 + 3x - 3x$ $11x - 13 > -5$ Why did we do that?
Because it helps us get closer to having $x$ all by itself!

STEP 4

Now, let's get rid of that $-13$ on the left side.
We can do this by adding $13$ to both sides: $11x - 13 + 13 > -5 + 13$ $11x > 8$ Awesome! We're almost there.

STEP 5

To finally isolate $x$ , we need to divide both sides of the inequality by $11$ : $\frac{11x}{11} > \frac{8}{11}$ $x > \frac{8}{11}$ And there we have it!

STEP 6

The solution to the inequality is $x > \frac{8}{11}$ .
So, the value of $A$ is $\frac{8}{11}$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the smallest value of xxx that makes the inequality 14x−13>−5+3x14x - 13 > -5 + 3x14x−13>−5+3x true. Watch out! Remember to flip the inequality sign if you multiply or divide both sides by a negative number!But we won't need to do that here.

STEP 2

1. Isolate the xxx terms.2. Isolate xxx.

STEP 3

STEP 4

Now, let's get rid of that −13-13−13 on the left side.We can do this by adding 131313 to both sides: 11x−13+13>−5+1311x - 13 + 13 > -5 + 1311x−13+13>−5+13 11x>811x > 811x>8Awesome! We're almost there.

STEP 5

To finally isolate xxx, we need to divide both sides of the inequality by 111111: 11x11>811 \frac{11x}{11} > \frac{8}{11} 1111x​>118​ x>811 x > \frac{8}{11} x>118​And there we have it!

STEP 6

The solution to the inequality is x>811x > \frac{8}{11}x>118​.So, the value of AAA is 811\frac{8}{11}118​.

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.

What is this asking? We need to find the smallest value of $x$ that makes the inequality $14x - 13 > -5 + 3x$ true. Watch out! Remember to flip the inequality sign if you multiply or divide both sides by a negative number!
But we won't need to do that here.

1. Isolate the $x$ terms.
2. Isolate $x$ .

Now, let's get rid of that $-13$ on the left side.
We can do this by adding $13$ to both sides: $11x - 13 + 13 > -5 + 13$ $11x > 8$ Awesome! We're almost there.

To finally isolate $x$ , we need to divide both sides of the inequality by $11$ : $\frac{11x}{11} > \frac{8}{11}$ $x > \frac{8}{11}$ And there we have it!

The solution to the inequality is $x > \frac{8}{11}$ .
So, the value of $A$ is $\frac{8}{11}$ .