Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-11x+15=8+x\)
- \(14x+8=10+9x\)
- \(-13x+11=5+x\)
- \(6x-5=11-11x\)
- \(8x+4=-6-7x\)
- \(4x+2=-8-7x\)
- \(4x+3=4+x\)
- \(-9x+14=13+x\)
- \(-7x+14=5+x\)
- \(-6x+13=2+x\)
- \(-9x-15=-15+x\)
- \(10x+3=9-13x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -11x \color{red}{+15}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-x }
& = & 8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 8 \color{blue}{-15} \\\Leftrightarrow &-12x
& = &-7\\\Leftrightarrow & \color{red}{-12}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+8}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8-9x }
& = & 10 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & 14x \color{blue}{-9x }
& = & 10 \color{blue}{-8} \\\Leftrightarrow &5x
& = &2\\\Leftrightarrow & \color{red}{5}x
& = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+11}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-x }
& = & 5 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 5 \color{blue}{-11} \\\Leftrightarrow &-14x
& = &-6\\\Leftrightarrow & \color{red}{-14}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-5}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5+11x }
& = & 11 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & 11 \color{blue}{+5} \\\Leftrightarrow &17x
& = &16\\\Leftrightarrow & \color{red}{17}x
& = &16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+4}& = & -6 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4+7x }
& = & -6 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 8x \color{blue}{+7x }
& = & -6 \color{blue}{-4} \\\Leftrightarrow &15x
& = &-10\\\Leftrightarrow & \color{red}{15}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{-10}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+2}& = & -8 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2+7x }
& = & -8 \color{red}{ -7x }\color{blue}{-2+7x } \\\Leftrightarrow & 4x \color{blue}{+7x }
& = & -8 \color{blue}{-2} \\\Leftrightarrow &11x
& = &-10\\\Leftrightarrow & \color{red}{11}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+3}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3-x }
& = & 4 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 4x \color{blue}{-x }
& = & 4 \color{blue}{-3} \\\Leftrightarrow &3x
& = &1\\\Leftrightarrow & \color{red}{3}x
& = &1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+14}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-x }
& = & 13 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 13 \color{blue}{-14} \\\Leftrightarrow &-10x
& = &-1\\\Leftrightarrow & \color{red}{-10}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-x }
& = & 5 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & 5 \color{blue}{-14} \\\Leftrightarrow &-8x
& = &-9\\\Leftrightarrow & \color{red}{-8}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+13}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-x }
& = & 2 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & 2 \color{blue}{-13} \\\Leftrightarrow &-7x
& = &-11\\\Leftrightarrow & \color{red}{-7}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-15}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-x }
& = & -15 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -15 \color{blue}{+15} \\\Leftrightarrow &-10x
& = &0\\\Leftrightarrow & \color{red}{-10}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+3}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3+13x }
& = & 9 \color{red}{ -13x }\color{blue}{-3+13x } \\\Leftrightarrow & 10x \color{blue}{+13x }
& = & 9 \color{blue}{-3} \\\Leftrightarrow &23x
& = &6\\\Leftrightarrow & \color{red}{23}x
& = &6\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{6}{23} \\\Leftrightarrow & \color{green}{ x = \frac{6}{23} } & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)