Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(2x+15=-6+x\)
- \(-14x-6=-12+x\)
- \(-4x-12=4+x\)
- \(-10x-15=-13+x\)
- \(5x-8=-15+12x\)
- \(-x+10=-14-10x\)
- \(x-6=-5+11x\)
- \(13x+4=9+8x\)
- \(11x-8=-12+10x\)
- \(13x+6=11+11x\)
- \(-3x+3=1+x\)
- \(-7x-4=-15+5x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 2x \color{red}{+15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-x }
& = & -6 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & -6 \color{blue}{-15} \\\Leftrightarrow &x
& = &-21\\\Leftrightarrow & \color{red}{}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -21 \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-6}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x }
& = & -12 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -12 \color{blue}{+6} \\\Leftrightarrow &-15x
& = &-6\\\Leftrightarrow & \color{red}{-15}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-12}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-12}\color{blue}{+12-x }
& = & 4 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & 4 \color{blue}{+12} \\\Leftrightarrow &-5x
& = &16\\\Leftrightarrow & \color{red}{-5}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-15}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-x }
& = & -13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -13 \color{blue}{+15} \\\Leftrightarrow &-11x
& = &2\\\Leftrightarrow & \color{red}{-11}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-8}& = & -15 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8-12x }
& = & -15 \color{red}{ +12x }\color{blue}{+8-12x } \\\Leftrightarrow & 5x \color{blue}{-12x }
& = & -15 \color{blue}{+8} \\\Leftrightarrow &-7x
& = &-7\\\Leftrightarrow & \color{red}{-7}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+10}& = & -14 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10+10x }
& = & -14 \color{red}{ -10x }\color{blue}{-10+10x } \\\Leftrightarrow & -x \color{blue}{+10x }
& = & -14 \color{blue}{-10} \\\Leftrightarrow &9x
& = &-24\\\Leftrightarrow & \color{red}{9}x
& = &-24\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-24}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-6}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6-11x }
& = & -5 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & x \color{blue}{-11x }
& = & -5 \color{blue}{+6} \\\Leftrightarrow &-10x
& = &1\\\Leftrightarrow & \color{red}{-10}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+4}& = & 9 \color{red}{ +8x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4-8x }
& = & 9 \color{red}{ +8x }\color{blue}{-4-8x } \\\Leftrightarrow & 13x \color{blue}{-8x }
& = & 9 \color{blue}{-4} \\\Leftrightarrow &5x
& = &5\\\Leftrightarrow & \color{red}{5}x
& = &5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{5}{5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-8}& = & -12 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8-10x }
& = & -12 \color{red}{ +10x }\color{blue}{+8-10x } \\\Leftrightarrow & 11x \color{blue}{-10x }
& = & -12 \color{blue}{+8} \\\Leftrightarrow &x
& = &-4\\\Leftrightarrow & \color{red}{}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -4 \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+6}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6-11x }
& = & 11 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & 13x \color{blue}{-11x }
& = & 11 \color{blue}{-6} \\\Leftrightarrow &2x
& = &5\\\Leftrightarrow & \color{red}{2}x
& = &5\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{5}{2} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+3}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-x }
& = & 1 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 1 \color{blue}{-3} \\\Leftrightarrow &-4x
& = &-2\\\Leftrightarrow & \color{red}{-4}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-4}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4-5x }
& = & -15 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & -7x \color{blue}{-5x }
& = & -15 \color{blue}{+4} \\\Leftrightarrow &-12x
& = &-11\\\Leftrightarrow & \color{red}{-12}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-11}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{12} } & & \\ & V = \left\{ \frac{11}{12} \right\} & \\\end{align}\)