Q 1. Is the equation true, false, or open? 3x + 1 = 22
(1 point)
• False; the expressions are never the same.
• Not enough information
• Open; there is a variable
• True; the expressions are the same for all values of the variable.
The equation "3x + 1 = 22" is true for a specific value of x, which is x = 7. However, it is important to note that the equation is not true for all values of x. Therefore, the correct answer is:
• Open; there is a variable
To determine if the equation 3x + 1 = 22 is true, false, or open, we need to solve it.
Step 1: Subtract 1 from both sides of the equation:
3x + 1 - 1 = 22 - 1
3x = 21
Step 2: Divide both sides of the equation by 3:
(3x) / 3 = 21 / 3
x = 7
Step 3: Substitute the value of x (which is 7) back into the original equation and check if both sides are equal:
3(7) + 1 = 22
21 + 1 = 22
22 = 22
Since both sides of the equation are equal, the equation 3x + 1 = 22 is true.
To determine whether the equation 3x + 1 = 22 is true, false, or open, we can solve it algebraically.
Step 1: Subtract 1 from both sides of the equation: 3x = 21.
Step 2: Divide both sides of the equation by 3: x = 7.
By solving the equation, we find that x = 7 satisfies the equation. When substituting x = 7 back into the equation, both sides are equal: 3(7) + 1 = 21 + 1 = 22.
Therefore, since there is a valid solution for x, the equation 3x + 1 = 22 is TRUE.