A binary operation \star on the set of real numbers is defined by a \star b = 3a + 2b - 1.… — JAMB UTME

A binary operation $\star$ on the set of real numbers is defined by $a \star b = 3a + 2b - 1$ . What is the value of $x$ such that $4 \star x = 25$ ?

The value of

x

7

Applying the binary operation definition

a \star b = 3a + 2b - 1

with

a = 4

and

b = x

gives

3(4) + 2x - 1 = 25

. Simplifying gives

2x + 11 = 25

, leading to

2x = 14

and

x = 7

Substitute

a = 4

and

b = x

into the definition of the binary operation

a \star b = 3a + 2b - 1

4 \star x = 3(4) + 2x - 1

Applying the given rule for the binary operation.

Simplify the expression on the left-hand side.

4 \star x = 12 + 2x - 1 = 2x + 11

Performing basic arithmetic multiplication and addition of constants.

Set the simplified expression equal to

25

and solve for

x

2x + 11 = 25 \implies 2x = 14 \implies x = 7

Subtracting

11

from both sides and dividing by

2

Evaluation of non-commutative binary operations and solving algebraic equations involving operational rules.

Question