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Solve the equation
Answer
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Graph
$y = 3 x + 1$
$y = 2 \left ( 2 x - 1 \right )$
$x$Intercept
$\left ( - \dfrac { 1 } { 3 } , 0 \right )$
$y$Intercept
$\left ( 0 , 1 \right )$
$x$Intercept
$\left ( \dfrac { 1 } { 2 } , 0 \right )$
$y$Intercept
$\left ( 0 , - 2 \right )$
$3x+1 = 2 \left( 2x-1 \right)$
$x = 3$
$ $ Solve a solution to $ x$
$3 x + 1 = \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right )$
$ $ Multiply each term in parentheses by $ 2$
$3 x + 1 = \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$3 x + 1 = \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ x } - 2$
$ $ Simplify the expression $ $
$3 x + 1 = \color{#FF6800}{ 4 } \color{#FF6800}{ x } - 2$
$3 x + 1 = \color{#FF6800}{ 4 } \color{#FF6800}{ x } - 2$
$ $ Move the variable to the left-hand side and change the symbol $ $
$3 x + 1 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } = - 2$
$3 x \color{#FF6800}{ + } \color{#FF6800}{ 1 } - 4 x = - 2$
$ $ Move the constant to the right side and change the sign $ $
$3 x - 4 x = - 2 \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } = - 2 - 1$
$ $ Organize the expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ x } = - 2 - 1$
$- x = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
$ $ Find the sum of the negative numbers $ $
$- x = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ - } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Change the sign of both sides of the equation $ $
$x = 3$
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