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