Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-6x+4=-8+x\)
- \(15x+6=-4+2x\)
- \(-3x-8=-9+x\)
- \(-15x-14=-7+13x\)
- \(7x-15=4-3x\)
- \(-5x+4=-6+x\)
- \(12x+13=11+5x\)
- \(11x+5=15-10x\)
- \(10x-15=-8-9x\)
- \(5x-5=4+8x\)
- \(x-9=-8+0x\)
- \(-11x+14=2+14x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -6x \color{red}{+4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-x }
& = & -8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -8 \color{blue}{-4} \\\Leftrightarrow &-7x
& = &-12\\\Leftrightarrow & \color{red}{-7}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+6}& = & -4 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6-2x }
& = & -4 \color{red}{ +2x }\color{blue}{-6-2x } \\\Leftrightarrow & 15x \color{blue}{-2x }
& = & -4 \color{blue}{-6} \\\Leftrightarrow &13x
& = &-10\\\Leftrightarrow & \color{red}{13}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-8}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8-x }
& = & -9 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -9 \color{blue}{+8} \\\Leftrightarrow &-4x
& = &-1\\\Leftrightarrow & \color{red}{-4}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-14}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-14}\color{blue}{+14-13x }
& = & -7 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & -7 \color{blue}{+14} \\\Leftrightarrow &-28x
& = &7\\\Leftrightarrow & \color{red}{-28}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{7}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-15}& = & 4 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15+3x }
& = & 4 \color{red}{ -3x }\color{blue}{+15+3x } \\\Leftrightarrow & 7x \color{blue}{+3x }
& = & 4 \color{blue}{+15} \\\Leftrightarrow &10x
& = &19\\\Leftrightarrow & \color{red}{10}x
& = &19\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{19}{10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4-x }
& = & -6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & -6 \color{blue}{-4} \\\Leftrightarrow &-6x
& = &-10\\\Leftrightarrow & \color{red}{-6}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+13}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13-5x }
& = & 11 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & 12x \color{blue}{-5x }
& = & 11 \color{blue}{-13} \\\Leftrightarrow &7x
& = &-2\\\Leftrightarrow & \color{red}{7}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+5}& = & 15 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5+10x }
& = & 15 \color{red}{ -10x }\color{blue}{-5+10x } \\\Leftrightarrow & 11x \color{blue}{+10x }
& = & 15 \color{blue}{-5} \\\Leftrightarrow &21x
& = &10\\\Leftrightarrow & \color{red}{21}x
& = &10\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}}
& = & \frac{10}{21} \\\Leftrightarrow & \color{green}{ x = \frac{10}{21} } & & \\ & V = \left\{ \frac{10}{21} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-15}& = & -8 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15+9x }
& = & -8 \color{red}{ -9x }\color{blue}{+15+9x } \\\Leftrightarrow & 10x \color{blue}{+9x }
& = & -8 \color{blue}{+15} \\\Leftrightarrow &19x
& = &7\\\Leftrightarrow & \color{red}{19}x
& = &7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-5}& = & 4 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5-8x }
& = & 4 \color{red}{ +8x }\color{blue}{+5-8x } \\\Leftrightarrow & 5x \color{blue}{-8x }
& = & 4 \color{blue}{+5} \\\Leftrightarrow &-3x
& = &9\\\Leftrightarrow & \color{red}{-3}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-9}& = & -8 \color{red}{ +0x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9+0x }
& = & -8 \color{red}{ +0x }\color{blue}{+9+0x } \\\Leftrightarrow & x \color{blue}{+0x }
& = & -8 \color{blue}{+9} \\\Leftrightarrow &x
& = &1\\\Leftrightarrow & \color{red}{}x
& = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+14}& = & 2 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+14}\color{blue}{-14-14x }
& = & 2 \color{red}{ +14x }\color{blue}{-14-14x } \\\Leftrightarrow & -11x \color{blue}{-14x }
& = & 2 \color{blue}{-14} \\\Leftrightarrow &-25x
& = &-12\\\Leftrightarrow & \color{red}{-25}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-12}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{12}{25} } & & \\ & V = \left\{ \frac{12}{25} \right\} & \\\end{align}\)