Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-4x-5=-14+x\)
- \(9x+8=5+8x\)
- \(-5x-3=2+x\)
- \(-2x-9=-13+13x\)
- \(-12x+1=-15+x\)
- \(12x+11=12-7x\)
- \(-4x-13=-1+9x\)
- \(14x-6=10-9x\)
- \(-x-15=15+8x\)
- \(6x-14=-9-5x\)
- \(-13x+12=10+x\)
- \(8x+6=13-15x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -4x \color{red}{-5}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-x }
& = & -14 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -14 \color{blue}{+5} \\\Leftrightarrow &-5x
& = &-9\\\Leftrightarrow & \color{red}{-5}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+8}& = & 5 \color{red}{ +8x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8-8x }
& = & 5 \color{red}{ +8x }\color{blue}{-8-8x } \\\Leftrightarrow & 9x \color{blue}{-8x }
& = & 5 \color{blue}{-8} \\\Leftrightarrow &x
& = &-3\\\Leftrightarrow & \color{red}{}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-3}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-x }
& = & 2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 2 \color{blue}{+3} \\\Leftrightarrow &-6x
& = &5\\\Leftrightarrow & \color{red}{-6}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-9}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-13x }
& = & -13 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -2x \color{blue}{-13x }
& = & -13 \color{blue}{+9} \\\Leftrightarrow &-15x
& = &-4\\\Leftrightarrow & \color{red}{-15}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-x }
& = & -15 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -15 \color{blue}{-1} \\\Leftrightarrow &-13x
& = &-16\\\Leftrightarrow & \color{red}{-13}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+11}& = & 12 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11+7x }
& = & 12 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 12x \color{blue}{+7x }
& = & 12 \color{blue}{-11} \\\Leftrightarrow &19x
& = &1\\\Leftrightarrow & \color{red}{19}x
& = &1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-13}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13-9x }
& = & -1 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -4x \color{blue}{-9x }
& = & -1 \color{blue}{+13} \\\Leftrightarrow &-13x
& = &12\\\Leftrightarrow & \color{red}{-13}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-6}& = & 10 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6+9x }
& = & 10 \color{red}{ -9x }\color{blue}{+6+9x } \\\Leftrightarrow & 14x \color{blue}{+9x }
& = & 10 \color{blue}{+6} \\\Leftrightarrow &23x
& = &16\\\Leftrightarrow & \color{red}{23}x
& = &16\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{16}{23} \\\Leftrightarrow & \color{green}{ x = \frac{16}{23} } & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-15}& = & 15 \color{red}{ +8x } \\\Leftrightarrow & -x \color{red}{-15}\color{blue}{+15-8x }
& = & 15 \color{red}{ +8x }\color{blue}{+15-8x } \\\Leftrightarrow & -x \color{blue}{-8x }
& = & 15 \color{blue}{+15} \\\Leftrightarrow &-9x
& = &30\\\Leftrightarrow & \color{red}{-9}x
& = &30\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{30}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-14}& = & -9 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14+5x }
& = & -9 \color{red}{ -5x }\color{blue}{+14+5x } \\\Leftrightarrow & 6x \color{blue}{+5x }
& = & -9 \color{blue}{+14} \\\Leftrightarrow &11x
& = &5\\\Leftrightarrow & \color{red}{11}x
& = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12-x }
& = & 10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 10 \color{blue}{-12} \\\Leftrightarrow &-14x
& = &-2\\\Leftrightarrow & \color{red}{-14}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+6}& = & 13 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6+15x }
& = & 13 \color{red}{ -15x }\color{blue}{-6+15x } \\\Leftrightarrow & 8x \color{blue}{+15x }
& = & 13 \color{blue}{-6} \\\Leftrightarrow &23x
& = &7\\\Leftrightarrow & \color{red}{23}x
& = &7\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{7}{23} \\\Leftrightarrow & \color{green}{ x = \frac{7}{23} } & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)