which equation is false 1.3x+2=83x+2=8 or 22x-5=102x−5=10
The false equation is 22x-5=10.
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To determine which equation is false, let's solve both equations and see which one results in a contradiction.
1) 1.3x + 2 = 8
Subtract 2 from both sides:
1.3x = 6
Divide both sides by 1.3:
x = 6/1.3 ≈ 4.615
2) 22x - 5 = 10
Add 5 to both sides:
22x = 15
Divide both sides by 22:
x = 15/22 ≈ 0.682
From the calculations, it is clear that the first equation (1.3x + 2 = 8) is false because the solution for x is approximately 4.615, not 4.615 as stated in the equation. Therefore, the false equation is 1.3x + 2 = 8.
To determine which equation is false, you need to solve both equations and evaluate if they are true or false.
Let's start with the first equation: 1.3x + 2 = 8
To solve this equation, we need to isolate the variable x.
First, we can subtract 2 from both sides:
1.3x = 8 - 2
1.3x = 6
Next, we divide both sides by 1.3 to find the value of x:
x = 6 / 1.3
x ≈ 4.615
Now, let's check the second equation: 22x - 5 = 10
To solve this equation, we need to isolate the variable x.
First, we can add 5 to both sides:
22x = 10 + 5
22x = 15
Next, we divide both sides by 22 to find the value of x:
x = 15 / 22
x ≈ 0.682
Upon solving both equations, we find the values of x. Now, we can substitute these values back into the original equations to check if they hold true.
1.3(4.615) + 2 = 8
6.00015 ≈ 8
22(0.682) - 5 = 10
10 = 10
Therefore, the first equation is false (1.3x + 2 = 8), while the second equation is true (22x - 5 = 10).