Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-4x+6=-7+x\)
- \(-11x-4=3+x\)
- \(-9x-14=3+14x\)
- \(-7x-6=2+4x\)
- \(-9x-2=7+x\)
- \(15x+8=5-2x\)
- \(-9x-10=4+x\)
- \(12x-8=-2+x\)
- \(-2x+15=10+x\)
- \(14x-9=4+x\)
- \(-5x-15=10+13x\)
- \(6x+2=13-5x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -4x \color{red}{+6}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-x }
& = & -7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -7 \color{blue}{-6} \\\Leftrightarrow &-5x
& = &-13\\\Leftrightarrow & \color{red}{-5}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-4}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-x }
& = & 3 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 3 \color{blue}{+4} \\\Leftrightarrow &-12x
& = &7\\\Leftrightarrow & \color{red}{-12}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{12} } & & \\ & V = \left\{ \frac{-7}{12} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-14}& = & 3 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-14x }
& = & 3 \color{red}{ +14x }\color{blue}{+14-14x } \\\Leftrightarrow & -9x \color{blue}{-14x }
& = & 3 \color{blue}{+14} \\\Leftrightarrow &-23x
& = &17\\\Leftrightarrow & \color{red}{-23}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{17}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{23} } & & \\ & V = \left\{ \frac{-17}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-6}& = & 2 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-4x }
& = & 2 \color{red}{ +4x }\color{blue}{+6-4x } \\\Leftrightarrow & -7x \color{blue}{-4x }
& = & 2 \color{blue}{+6} \\\Leftrightarrow &-11x
& = &8\\\Leftrightarrow & \color{red}{-11}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-2}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-2}\color{blue}{+2-x }
& = & 7 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 7 \color{blue}{+2} \\\Leftrightarrow &-10x
& = &9\\\Leftrightarrow & \color{red}{-10}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+8}& = & 5 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+8}\color{blue}{-8+2x }
& = & 5 \color{red}{ -2x }\color{blue}{-8+2x } \\\Leftrightarrow & 15x \color{blue}{+2x }
& = & 5 \color{blue}{-8} \\\Leftrightarrow &17x
& = &-3\\\Leftrightarrow & \color{red}{17}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-10}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10-x }
& = & 4 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 4 \color{blue}{+10} \\\Leftrightarrow &-10x
& = &14\\\Leftrightarrow & \color{red}{-10}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8-x }
& = & -2 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & -2 \color{blue}{+8} \\\Leftrightarrow &11x
& = &6\\\Leftrightarrow & \color{red}{11}x
& = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+15}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15-x }
& = & 10 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & 10 \color{blue}{-15} \\\Leftrightarrow &-3x
& = &-5\\\Leftrightarrow & \color{red}{-3}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-9}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9-x }
& = & 4 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & 4 \color{blue}{+9} \\\Leftrightarrow &13x
& = &13\\\Leftrightarrow & \color{red}{13}x
& = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-15}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-13x }
& = & 10 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -5x \color{blue}{-13x }
& = & 10 \color{blue}{+15} \\\Leftrightarrow &-18x
& = &25\\\Leftrightarrow & \color{red}{-18}x
& = &25\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}}
& = & \frac{25}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{18} } & & \\ & V = \left\{ \frac{-25}{18} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+2}& = & 13 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2+5x }
& = & 13 \color{red}{ -5x }\color{blue}{-2+5x } \\\Leftrightarrow & 6x \color{blue}{+5x }
& = & 13 \color{blue}{-2} \\\Leftrightarrow &11x
& = &11\\\Leftrightarrow & \color{red}{11}x
& = &11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{11}{11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)