To solve the inequality x - 2.41 > 4.76, we need to isolate the variable x.
Adding 2.41 to both sides, we have:
x - 2.41 + 2.41 > 4.76 + 2.41
Simplifying,
x > 7.17
Therefore, the solution to the inequality is x > 7.17.
x−2.41>4.76
11 answers
What is the solution set for 16.5≥1.25x+12.75 ?
To find the solution set for the inequality 16.5 ≥ 1.25x + 12.75, we need to isolate the variable x.
First, subtract 12.75 from both sides:
16.5 - 12.75 ≥ 1.25x + 12.75 - 12.75
This simplifies to:
3.75 ≥ 1.25x
Next, divide both sides by 1.25 to solve for x:
3.75/1.25 ≥ 1.25x/1.25
This simplifies to:
3 ≥ x
Therefore, the solution set for the inequality is x ≤ 3.
First, subtract 12.75 from both sides:
16.5 - 12.75 ≥ 1.25x + 12.75 - 12.75
This simplifies to:
3.75 ≥ 1.25x
Next, divide both sides by 1.25 to solve for x:
3.75/1.25 ≥ 1.25x/1.25
This simplifies to:
3 ≥ x
Therefore, the solution set for the inequality is x ≤ 3.
What is the solution set for −4x−5<31?
To find the solution set for the inequality -4x - 5 < 31, we need to isolate the variable x.
First, we'll add 5 to both sides:
-4x - 5 + 5 < 31 + 5
This simplifies to:
-4x < 36
Next, we'll divide both sides by -4. Since we divide by a negative number, we need to reverse the inequality sign:
-4x / -4 > 36 / -4
This simplifies to:
x > -9
Therefore, the solution set for the inequality is x > -9.
First, we'll add 5 to both sides:
-4x - 5 + 5 < 31 + 5
This simplifies to:
-4x < 36
Next, we'll divide both sides by -4. Since we divide by a negative number, we need to reverse the inequality sign:
-4x / -4 > 36 / -4
This simplifies to:
x > -9
Therefore, the solution set for the inequality is x > -9.
Solve for x in the inequality.
−1.7x≥5.95
−1.7x≥5.95
To solve the inequality -1.7x ≥ 5.95, we need to isolate the variable x.
First, we'll divide both sides of the inequality by -1.7. Since we divide by a negative number, we need to reverse the inequality sign:
-1.7x / -1.7 ≤ 5.95 / -1.7
This simplifies to:
x ≤ -3.5
Therefore, the solution set for the inequality is x ≤ -3.5.
First, we'll divide both sides of the inequality by -1.7. Since we divide by a negative number, we need to reverse the inequality sign:
-1.7x / -1.7 ≤ 5.95 / -1.7
This simplifies to:
x ≤ -3.5
Therefore, the solution set for the inequality is x ≤ -3.5.
Jake begins the summer with 1,000 marbles in his collection. He aims to have a minimum of 500 marbles left by the end of the summer. Each week, he gives away 100 marbles to friends. Write an inequality to determine the number of weeks Jake can continue giving away marbles and find the solution.(1 point)
Let w represent the number of weeks Jake can continue giving away marbles.
Each week, Jake gives away 100 marbles, so the number of marbles left can be represented as 1000 - 100w.
To find the number of weeks Jake can continue giving away marbles, we need to ensure that the number of marbles left is greater than or equal to 500, so the inequality is:
1000 - 100w ≥ 500
Now, we can solve for w:
1000 - 100w ≥ 500
-100w ≥ 500 - 1000
-100w ≥ -500
w ≤ (-500)/(-100)
w ≤ 5
Therefore, the solution to the inequality is w ≤ 5, meaning that Jake can continue giving away marbles for a maximum of 5 weeks.
Each week, Jake gives away 100 marbles, so the number of marbles left can be represented as 1000 - 100w.
To find the number of weeks Jake can continue giving away marbles, we need to ensure that the number of marbles left is greater than or equal to 500, so the inequality is:
1000 - 100w ≥ 500
Now, we can solve for w:
1000 - 100w ≥ 500
-100w ≥ 500 - 1000
-100w ≥ -500
w ≤ (-500)/(-100)
w ≤ 5
Therefore, the solution to the inequality is w ≤ 5, meaning that Jake can continue giving away marbles for a maximum of 5 weeks.
Jake begins the summer with 1,000 marbles in his collection. He aims to have a minimum of 500 marbles left by the end of the summer. Each week, he gives away 100 marbles to friends. Write an inequality to determine the number of weeks Jake can continue giving away marbles and find the solution.(1 point)
Responses
1000−100w≥500; w≥51000−100w≥500; w≥5
1000−100w≥500; w≤51000−100w≥500; w≤5
1000−100w≤500; w≥61000−100w≤500; w≥6
1000+100w≥500; w≥6
Responses
1000−100w≥500; w≥51000−100w≥500; w≥5
1000−100w≥500; w≤51000−100w≥500; w≤5
1000−100w≤500; w≥61000−100w≤500; w≥6
1000+100w≥500; w≥6
The correct inequality is 1000 - 100w ≥ 500, as Jake wants to have a minimum of 500 marbles left.
To solve for the number of weeks Jake can continue giving away marbles, we can simplify the inequality:
1000 - 100w ≥ 500
Subtract 1000 from both sides:
-100w ≥ -500
Divide by -100, remembering to flip the inequality sign:
w ≤ 5
Therefore, the correct solution to the inequality is w ≤ 5. This means that Jake can continue giving away marbles for a maximum of 5 weeks.
To solve for the number of weeks Jake can continue giving away marbles, we can simplify the inequality:
1000 - 100w ≥ 500
Subtract 1000 from both sides:
-100w ≥ -500
Divide by -100, remembering to flip the inequality sign:
w ≤ 5
Therefore, the correct solution to the inequality is w ≤ 5. This means that Jake can continue giving away marbles for a maximum of 5 weeks.