Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-8x-1=6+x\)
- \(-3x+6=-6+x\)
- \(-12x+13=-13+x\)
- \(-10x+2=-4+7x\)
- \(-3x+3=-5+7x\)
- \(-3x+3=-7+13x\)
- \(15x+7=13+4x\)
- \(-8x+1=-15+x\)
- \(-x+12=15+6x\)
- \(13x-13=11+10x\)
- \(-5x-11=14+11x\)
- \(-8x-4=-7+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -8x \color{red}{-1}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-x }
& = & 6 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 6 \color{blue}{+1} \\\Leftrightarrow &-9x
& = &7\\\Leftrightarrow & \color{red}{-9}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+6}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6-x }
& = & -6 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -6 \color{blue}{-6} \\\Leftrightarrow &-4x
& = &-12\\\Leftrightarrow & \color{red}{-4}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-12}{-4} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+13}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-x }
& = & -13 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -13 \color{blue}{-13} \\\Leftrightarrow &-13x
& = &-26\\\Leftrightarrow & \color{red}{-13}x
& = &-26\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-26}{-13} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+2}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-7x }
& = & -4 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & -10x \color{blue}{-7x }
& = & -4 \color{blue}{-2} \\\Leftrightarrow &-17x
& = &-6\\\Leftrightarrow & \color{red}{-17}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+3}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-7x }
& = & -5 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -3x \color{blue}{-7x }
& = & -5 \color{blue}{-3} \\\Leftrightarrow &-10x
& = &-8\\\Leftrightarrow & \color{red}{-10}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+3}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-13x }
& = & -7 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & -3x \color{blue}{-13x }
& = & -7 \color{blue}{-3} \\\Leftrightarrow &-16x
& = &-10\\\Leftrightarrow & \color{red}{-16}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+7}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7-4x }
& = & 13 \color{red}{ +4x }\color{blue}{-7-4x } \\\Leftrightarrow & 15x \color{blue}{-4x }
& = & 13 \color{blue}{-7} \\\Leftrightarrow &11x
& = &6\\\Leftrightarrow & \color{red}{11}x
& = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x }
& = & -15 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & -15 \color{blue}{-1} \\\Leftrightarrow &-9x
& = &-16\\\Leftrightarrow & \color{red}{-9}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+12}& = & 15 \color{red}{ +6x } \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12-6x }
& = & 15 \color{red}{ +6x }\color{blue}{-12-6x } \\\Leftrightarrow & -x \color{blue}{-6x }
& = & 15 \color{blue}{-12} \\\Leftrightarrow &-7x
& = &3\\\Leftrightarrow & \color{red}{-7}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-13}& = & 11 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{-13}\color{blue}{+13-10x }
& = & 11 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & 13x \color{blue}{-10x }
& = & 11 \color{blue}{+13} \\\Leftrightarrow &3x
& = &24\\\Leftrightarrow & \color{red}{3}x
& = &24\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{24}{3} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-11}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-11x }
& = & 14 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & -5x \color{blue}{-11x }
& = & 14 \color{blue}{+11} \\\Leftrightarrow &-16x
& = &25\\\Leftrightarrow & \color{red}{-16}x
& = &25\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{25}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{16} } & & \\ & V = \left\{ \frac{-25}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-4}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-x }
& = & -7 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & -7 \color{blue}{+4} \\\Leftrightarrow &-9x
& = &-3\\\Leftrightarrow & \color{red}{-9}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)