Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(x+9=8-2x\)
- \(-13x-6=6+x\)
- \(-12x+14=7+x\)
- \(-5x+3=12+x\)
- \(-3x-9=-2+x\)
- \(3x-1=-5-2x\)
- \(4x-4=-1-15x\)
- \(-10x-11=-2+x\)
- \(7x+4=-11+x\)
- \(-5x+9=-13+13x\)
- \(-6x+5=-15+x\)
- \(-11x-12=5+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & x \color{red}{+9}& = & 8 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9+2x }
& = & 8 \color{red}{ -2x }\color{blue}{-9+2x } \\\Leftrightarrow & x \color{blue}{+2x }
& = & 8 \color{blue}{-9} \\\Leftrightarrow &3x
& = &-1\\\Leftrightarrow & \color{red}{3}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{-1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-x }
& = & 6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 6 \color{blue}{+6} \\\Leftrightarrow &-14x
& = &12\\\Leftrightarrow & \color{red}{-14}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-x }
& = & 7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 7 \color{blue}{-14} \\\Leftrightarrow &-13x
& = &-7\\\Leftrightarrow & \color{red}{-13}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+3}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-x }
& = & 12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 12 \color{blue}{-3} \\\Leftrightarrow &-6x
& = &9\\\Leftrightarrow & \color{red}{-6}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-9}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-x }
& = & -2 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -2 \color{blue}{+9} \\\Leftrightarrow &-4x
& = &7\\\Leftrightarrow & \color{red}{-4}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-1}& = & -5 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1+2x }
& = & -5 \color{red}{ -2x }\color{blue}{+1+2x } \\\Leftrightarrow & 3x \color{blue}{+2x }
& = & -5 \color{blue}{+1} \\\Leftrightarrow &5x
& = &-4\\\Leftrightarrow & \color{red}{5}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-4}& = & -1 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4+15x }
& = & -1 \color{red}{ -15x }\color{blue}{+4+15x } \\\Leftrightarrow & 4x \color{blue}{+15x }
& = & -1 \color{blue}{+4} \\\Leftrightarrow &19x
& = &3\\\Leftrightarrow & \color{red}{19}x
& = &3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-11}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-x }
& = & -2 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -2 \color{blue}{+11} \\\Leftrightarrow &-11x
& = &9\\\Leftrightarrow & \color{red}{-11}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+4}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4-x }
& = & -11 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 7x \color{blue}{-x }
& = & -11 \color{blue}{-4} \\\Leftrightarrow &6x
& = &-15\\\Leftrightarrow & \color{red}{6}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}}
& = & \frac{-15}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+9}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9-13x }
& = & -13 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & -5x \color{blue}{-13x }
& = & -13 \color{blue}{-9} \\\Leftrightarrow &-18x
& = &-22\\\Leftrightarrow & \color{red}{-18}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}}
& = & \frac{-22}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+5}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-x }
& = & -15 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -15 \color{blue}{-5} \\\Leftrightarrow &-7x
& = &-20\\\Leftrightarrow & \color{red}{-7}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-20}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{20}{7} } & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12-x }
& = & 5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 5 \color{blue}{+12} \\\Leftrightarrow &-12x
& = &17\\\Leftrightarrow & \color{red}{-12}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{17}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{12} } & & \\ & V = \left\{ \frac{-17}{12} \right\} & \\\end{align}\)