To determine which of the following expressions is not a linear equation, we need to understand the definition of a linear equation. A linear equation is an equation of the form [tex]\(Ax + B = 0\)[/tex] or [tex]\(Ax + By + C = 0\)[/tex], where [tex]\(A\)[/tex], [tex]\(B\)[/tex], and [tex]\(C\)[/tex] are constants, and [tex]\(x\)[/tex] and [tex]\(y\)[/tex] are variables.
Let's analyze each option:
(a) [tex]\(2x + 5 = 1\)[/tex]
We can rewrite this equation to fit the standard form:
[tex]\[2x + 5 - 1 = 0\][/tex]
[tex]\[2x + 4 = 0\][/tex]
This is a standard linear equation.
(b) [tex]\(x - 1 = 0\)[/tex]
This fits the form [tex]\(Ax + B = 0\)[/tex] directly:
[tex]\[x - 1 = 0\][/tex]
This is a linear equation.
(c) [tex]\(y + 1 = 0\)[/tex]
This can also be written as:
[tex]\[y + 1 = 0\][/tex]
It also fits the linear equation form.
(d) [tex]\(5x + 3\)[/tex]
This is an expression rather than an equation because it doesn't have an equality sign ('=') and cannot be written in the form [tex]\(Ax + B = 0\)[/tex]:
Given this analysis, the option that is not a linear equation is:
(d) [tex]\(5x + 3\)[/tex]
