Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(5x-2=-13-7x\)
- \(4x+1=14+3x\)
- \(-9x-3=-4+x\)
- \(-4x+4=-7+x\)
- \(-9x+15=-12+14x\)
- \(11x-13=-4-7x\)
- \(-13x+8=-5+14x\)
- \(-x+8=14+5x\)
- \(7x+13=4-13x\)
- \(-6x-8=-2+x\)
- \(-4x-7=-15+9x\)
- \(3x-10=-7+7x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 5x \color{red}{-2}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2+7x }
& = & -13 \color{red}{ -7x }\color{blue}{+2+7x } \\\Leftrightarrow & 5x \color{blue}{+7x }
& = & -13 \color{blue}{+2} \\\Leftrightarrow &12x
& = &-11\\\Leftrightarrow & \color{red}{12}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}}
& = & \frac{-11}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+1}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1-3x }
& = & 14 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & 4x \color{blue}{-3x }
& = & 14 \color{blue}{-1} \\\Leftrightarrow &x
& = &13\\\Leftrightarrow & \color{red}{}x
& = &13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 13 \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-3}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-x }
& = & -4 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -4 \color{blue}{+3} \\\Leftrightarrow &-10x
& = &-1\\\Leftrightarrow & \color{red}{-10}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+4}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x }
& = & -7 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -7 \color{blue}{-4} \\\Leftrightarrow &-5x
& = &-11\\\Leftrightarrow & \color{red}{-5}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+15}& = & -12 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-14x }
& = & -12 \color{red}{ +14x }\color{blue}{-15-14x } \\\Leftrightarrow & -9x \color{blue}{-14x }
& = & -12 \color{blue}{-15} \\\Leftrightarrow &-23x
& = &-27\\\Leftrightarrow & \color{red}{-23}x
& = &-27\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{-27}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{27}{23} } & & \\ & V = \left\{ \frac{27}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-13}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13+7x }
& = & -4 \color{red}{ -7x }\color{blue}{+13+7x } \\\Leftrightarrow & 11x \color{blue}{+7x }
& = & -4 \color{blue}{+13} \\\Leftrightarrow &18x
& = &9\\\Leftrightarrow & \color{red}{18}x
& = &9\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}}
& = & \frac{9}{18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+8}& = & -5 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-14x }
& = & -5 \color{red}{ +14x }\color{blue}{-8-14x } \\\Leftrightarrow & -13x \color{blue}{-14x }
& = & -5 \color{blue}{-8} \\\Leftrightarrow &-27x
& = &-13\\\Leftrightarrow & \color{red}{-27}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}}
& = & \frac{-13}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{13}{27} } & & \\ & V = \left\{ \frac{13}{27} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+8}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{+8}\color{blue}{-8-5x }
& = & 14 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & -x \color{blue}{-5x }
& = & 14 \color{blue}{-8} \\\Leftrightarrow &-6x
& = &6\\\Leftrightarrow & \color{red}{-6}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{6}{-6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+13}& = & 4 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+13}\color{blue}{-13+13x }
& = & 4 \color{red}{ -13x }\color{blue}{-13+13x } \\\Leftrightarrow & 7x \color{blue}{+13x }
& = & 4 \color{blue}{-13} \\\Leftrightarrow &20x
& = &-9\\\Leftrightarrow & \color{red}{20}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{-9}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{20} } & & \\ & V = \left\{ \frac{-9}{20} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-8}\color{blue}{+8-x }
& = & -2 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -2 \color{blue}{+8} \\\Leftrightarrow &-7x
& = &6\\\Leftrightarrow & \color{red}{-7}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-7}& = & -15 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-9x }
& = & -15 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & -4x \color{blue}{-9x }
& = & -15 \color{blue}{+7} \\\Leftrightarrow &-13x
& = &-8\\\Leftrightarrow & \color{red}{-13}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-10}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{-10}\color{blue}{+10-7x }
& = & -7 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & 3x \color{blue}{-7x }
& = & -7 \color{blue}{+10} \\\Leftrightarrow &-4x
& = &3\\\Leftrightarrow & \color{red}{-4}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)