QuestionFind the operation $\circ$ such that $-.64 \circ ? = 1.29$ . What is $?$

Studdy Solution

STEP 1

Assumptions1. The unknown operation is denoted as $\circ$ . The operation $\circ$ is a binary operation, i.e., it takes two operands3. The equation is $-.64 \circ ? =1.29$
4. We need to find the value that, when operated on $-.64$ with the operation $\circ$ , gives $1.29$

STEP 2

Let's denote the unknown value as $x$ . So, the equation becomes $-.64 \circ x =1.29$

STEP 3

Since we don't know the operation $\circ$ , let's assume it to be addition, subtraction, multiplication, or division and solve for $x$ in each case.

STEP 4

If $\circ$ is addition, the equation becomes $-.64 + x =1.29$

STEP 5

To isolate $x$ , subtract $-.64$ from both sides of the equation $x =1.29 - (-.64)$

STEP 6

Calculate the value of $x$ $x =1.29 - (-.64) =1.29 + .64 =1.93$ So, if $\circ$ is addition, $x =1.93$ .

STEP 7

If $\circ$ is subtraction, the equation becomes $-.64 - x =1.29$

STEP 8

To isolate $x$ , add $-.64$ to both sides of the equation and multiply by $-1$ $x = -1.29 - (-.64)$

STEP 9

Calculate the value of $x$ $x = -.29 - (-.64) = -.29 + .64 = -.65$ So, if $\circ$ is subtraction, $x = -.65$ .

STEP 10

If $\circ$ is multiplication, the equation becomes $-.64 \times x =.29$

STEP 11

To isolate $x$ , divide both sides of the equation by $-.64$ $x = \frac{.29}{-.64}$

STEP 12

Calculate the value of $x$ $x = \frac{.29}{-.64} = -2.015625$ So, if $\circ$ is multiplication, $x = -2.015625$ .

STEP 13

If $\circ$ is division, the equation becomes $\frac{-.64}{x} =.29$

STEP 14

To isolate $x$ , multiply both sides of the equation by $x$ and divide by $.29$ $x = \frac{-.64}{.29}$

STEP 15

Calculate the value of $x$ $x = \frac{-.64}{.29} = -0.49612403100775193$ So, if $\circ$ is division, $x = -0.49612403100775193$ .

STEP 16

Thus, depending on the operation $\circ$ , the value of $x$ can be $.93$ , $-0.65$ , $-2.015625$ , or $-0.49612403100775193$ .

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