Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-9x+12=15+x\)
- \(8x+12=-10+x\)
- \(5x-7=14-2x\)
- \(-4x-7=-15+9x\)
- \(4x+1=-5+9x\)
- \(-11x+2=-12+x\)
- \(2x-5=4+x\)
- \(-5x-11=10+8x\)
- \(-13x-6=-9+x\)
- \(-7x-14=-2+11x\)
- \(-7x+14=-13+11x\)
- \(-x-8=4-15x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -9x \color{red}{+12}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12-x }
& = & 15 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 15 \color{blue}{-12} \\\Leftrightarrow &-10x
& = &3\\\Leftrightarrow & \color{red}{-10}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+12}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12-x }
& = & -10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 8x \color{blue}{-x }
& = & -10 \color{blue}{-12} \\\Leftrightarrow &7x
& = &-22\\\Leftrightarrow & \color{red}{7}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{-22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-7}& = & 14 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7+2x }
& = & 14 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & 5x \color{blue}{+2x }
& = & 14 \color{blue}{+7} \\\Leftrightarrow &7x
& = &21\\\Leftrightarrow & \color{red}{7}x
& = &21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{21}{7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-7}& = & -15 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-9x }
& = & -15 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & -4x \color{blue}{-9x }
& = & -15 \color{blue}{+7} \\\Leftrightarrow &-13x
& = &-8\\\Leftrightarrow & \color{red}{-13}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+1}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1-9x }
& = & -5 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & 4x \color{blue}{-9x }
& = & -5 \color{blue}{-1} \\\Leftrightarrow &-5x
& = &-6\\\Leftrightarrow & \color{red}{-5}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+2}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-x }
& = & -12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -12 \color{blue}{-2} \\\Leftrightarrow &-12x
& = &-14\\\Leftrightarrow & \color{red}{-12}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-5}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-x }
& = & 4 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & 4 \color{blue}{+5} \\\Leftrightarrow &x
& = &9\\\Leftrightarrow & \color{red}{}x
& = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-11}& = & 10 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-8x }
& = & 10 \color{red}{ +8x }\color{blue}{+11-8x } \\\Leftrightarrow & -5x \color{blue}{-8x }
& = & 10 \color{blue}{+11} \\\Leftrightarrow &-13x
& = &21\\\Leftrightarrow & \color{red}{-13}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{21}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{13} } & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-6}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-x }
& = & -9 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -9 \color{blue}{+6} \\\Leftrightarrow &-14x
& = &-3\\\Leftrightarrow & \color{red}{-14}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-14}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-11x }
& = & -2 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & -7x \color{blue}{-11x }
& = & -2 \color{blue}{+14} \\\Leftrightarrow &-18x
& = &12\\\Leftrightarrow & \color{red}{-18}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}}
& = & \frac{12}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+14}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-11x }
& = & -13 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & -7x \color{blue}{-11x }
& = & -13 \color{blue}{-14} \\\Leftrightarrow &-18x
& = &-27\\\Leftrightarrow & \color{red}{-18}x
& = &-27\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}}
& = & \frac{-27}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-8}& = & 4 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-8}\color{blue}{+8+15x }
& = & 4 \color{red}{ -15x }\color{blue}{+8+15x } \\\Leftrightarrow & -x \color{blue}{+15x }
& = & 4 \color{blue}{+8} \\\Leftrightarrow &14x
& = &12\\\Leftrightarrow & \color{red}{14}x
& = &12\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{12}{14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)