Algebraic Equations and Inequalities

Placing an equals sign between two algebraic expressions implies that they have the same numerical value <math display='block'> <mrow> <mn>2</mn><mi>x</mi><mo>=</mo><mn>10</mn><mo>,</mo><mtext>&#x2003;</mtext><mtext>&#x2003;</mtext><mn>3</mn><mi>x</mi><mo>&#x2212;</mo><mn>2</mn><mo>=</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo>,</mo><mtext>&#x2003;</mtext><mtext>&#x2003;</mtext><msup> <mi>x</mi> <mn>2</mn> </msup> <mo>&#x2212;</mo><mn>5</mn><mi>x</mi><mo>&#x2212;</mo><mn>6</mn><mo>=</mo><mn>0</mn> </mrow> </math>$$2x=10,\quad \quad 3x-2=x+4,\quad \quad {{x}^{2}}-5x-6=0$$ are all equations in one unknown, x, which is called the variable. In order to maintain the equality, whatever change is made to the expression on one side of an equation must also be made on the other side.