which equation is false 1.3x+2=83x+2=8 or 22x-5=102x−5=10 including multiple equals signs
The equation that is false is 1.3x + 2 = 8.
To see why this equation is false, let's solve it step-by-step:
1.3x + 2 = 8
Subtract 2 from both sides:
1.3x = 6
Now divide both sides by 1.3:
x = 6/1.3
Using a calculator, we can find that x ≈ 4.615.
Now, let's substitute this value of x into the original equation:
1.3(4.615) + 2 = 8
Simplifying further, we get:
5.9995 + 2 = 8
This equation is not true because 5.9995 + 2 is not equal to 8.
The given equations are:
1) 1.3x + 2 = 8
2) 22x - 5 = 10
We need to determine which one of these equations is false.
Let's solve each equation step-by-step:
1) 1.3x + 2 = 8
Subtract 2 from both sides:
1.3x = 8 - 2
1.3x = 6
To isolate x, divide both sides by 1.3:
x = 6 / 1.3
x ≈ 4.615
2) 22x - 5 = 10
Add 5 to both sides:
22x = 10 + 5
22x = 15
To isolate x, divide both sides by 22:
x = 15 / 22
x ≈ 0.682
Comparing the solutions obtained for each equation, we find that neither equation is false. Thus, both equations hold true.
To determine which equation is false among the given options, we need to solve each equation and check if the resulting values satisfy the equation. Let's go through each equation separately:
1) 1.3x + 2 = 8
To solve this equation, we'll first subtract 2 from both sides to isolate the term containing the variable:
1.3x = 6
Next, we'll divide both sides by 1.3 to solve for x:
x = 6 / 1.3
Using a calculator, we can find that x is approximately 4.615.
Now, let's substitute this value back into the equation and check if it holds true:
1.3(4.615) + 2 = 8
5.9995 + 2 ≈ 8
7.9995 ≈ 8
Since the left side is approximately equal to the right side, this equation is true.
2) 22x - 5 = 10
To solve this equation, we'll first add 5 to both sides:
22x = 15
Next, we'll divide both sides by 22 to solve for x:
x = 15 / 22
Using a calculator, we can find that x is approximately 0.682.
Now, let's substitute this value back into the equation and check if it holds true:
22(0.682) - 5 = 10
14.964 - 5 = 10
9.964 ≠ 10
Since the left side is not equal to the right side, this equation is false.
Therefore, the false equation is 22x - 5 = 10.