Ex 3:
4x-7<2x+5
4x-7-2x<2x-2x+5
2x-7<5
2x-7+7<5+7
2x<12
2x/2<12/2
x< 6 Note I did not switch the order of the inequality here since I divided by a positive number. Multiplying or dividing by a positive number does not change the order of the inequality.
So x has to be less than or equal to 6. So 5 should work well and so should 6.
Check:
4(6)-7<2(6)+5
24-7<12+5
17<17
This is true since 17=17 so it looks like 6 is the correct cut off.
Check:
5 should work too.
4(5)-7<2(5)+5
20-7<10+5
13<15
This is also true so it looks like my answer is correct so the answer is {x|x < 6} which again is read "The set of all values for x such that x is less than or equal to 6.”
To solve the inequality 4x-7<2x+5, you need to isolate the variable x on one side of the inequality sign. Here's how you can solve it step by step:
Step 1: Start by subtracting 2x from both sides of the inequality to eliminate the variable term on the right side: 4x - 7 - 2x < 2x - 2x + 5 becomes 2x - 7 < 5.
Step 2: Next, add 7 to both sides of the inequality to move the constant term to the right side: 2x - 7 + 7 < 5 + 7 becomes 2x < 12.
Step 3: Divide both sides of the inequality by 2 to solve for x: 2x/2 < 12/2 becomes x < 6. Remember, you don't need to switch the order of the inequality since you divided by a positive number.
So, the solution to the inequality 4x-7<2x+5 is x < 6. This means that all values of x that are less than 6 satisfy the inequality.
To check if this solution is correct, you can substitute values of x that are less than 6, such as 5 and 6, back into the original inequality:
1. For x = 5:
4(5) - 7 < 2(5) + 5 becomes 20 - 7 < 10 + 5, which simplifies to 13 < 15. This is true, so 5 satisfies the inequality.
2. For x = 6:
4(6) - 7 < 2(6) + 5 becomes 24 - 7 < 12 + 5, which simplifies to 17 < 17. This is not true, so 6 does not satisfy the inequality.
Based on the check, you can conclude that the correct solution is x < 6.