Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(6x+4=-13-5x\)
- \(-8x+15=-9+x\)
- \(15x+12=-13+11x\)
- \(8x-4=-3+3x\)
- \(6x-13=8-5x\)
- \(-7x-8=-14+x\)
- \(4x-15=7+x\)
- \(-12x-9=10+x\)
- \(10x-2=-1-9x\)
- \(-4x-9=-5+x\)
- \(-2x-15=-8+5x\)
- \(-3x-14=2+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 6x \color{red}{+4}& = & -13 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4+5x }
& = & -13 \color{red}{ -5x }\color{blue}{-4+5x } \\\Leftrightarrow & 6x \color{blue}{+5x }
& = & -13 \color{blue}{-4} \\\Leftrightarrow &11x
& = &-17\\\Leftrightarrow & \color{red}{11}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+15}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-x }
& = & -9 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & -9 \color{blue}{-15} \\\Leftrightarrow &-9x
& = &-24\\\Leftrightarrow & \color{red}{-9}x
& = &-24\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-24}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+12}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+12}\color{blue}{-12-11x }
& = & -13 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 15x \color{blue}{-11x }
& = & -13 \color{blue}{-12} \\\Leftrightarrow &4x
& = &-25\\\Leftrightarrow & \color{red}{4}x
& = &-25\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{-25}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{4} } & & \\ & V = \left\{ \frac{-25}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-4}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4-3x }
& = & -3 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & 8x \color{blue}{-3x }
& = & -3 \color{blue}{+4} \\\Leftrightarrow &5x
& = &1\\\Leftrightarrow & \color{red}{5}x
& = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-13}& = & 8 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13+5x }
& = & 8 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 6x \color{blue}{+5x }
& = & 8 \color{blue}{+13} \\\Leftrightarrow &11x
& = &21\\\Leftrightarrow & \color{red}{11}x
& = &21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-x }
& = & -14 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -14 \color{blue}{+8} \\\Leftrightarrow &-8x
& = &-6\\\Leftrightarrow & \color{red}{-8}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-15}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15-x }
& = & 7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 4x \color{blue}{-x }
& = & 7 \color{blue}{+15} \\\Leftrightarrow &3x
& = &22\\\Leftrightarrow & \color{red}{3}x
& = &22\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{22}{3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-9}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-9}\color{blue}{+9-x }
& = & 10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 10 \color{blue}{+9} \\\Leftrightarrow &-13x
& = &19\\\Leftrightarrow & \color{red}{-13}x
& = &19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-2}& = & -1 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2+9x }
& = & -1 \color{red}{ -9x }\color{blue}{+2+9x } \\\Leftrightarrow & 10x \color{blue}{+9x }
& = & -1 \color{blue}{+2} \\\Leftrightarrow &19x
& = &1\\\Leftrightarrow & \color{red}{19}x
& = &1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-9}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-x }
& = & -5 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -5 \color{blue}{+9} \\\Leftrightarrow &-5x
& = &4\\\Leftrightarrow & \color{red}{-5}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-15}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-5x }
& = & -8 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & -2x \color{blue}{-5x }
& = & -8 \color{blue}{+15} \\\Leftrightarrow &-7x
& = &7\\\Leftrightarrow & \color{red}{-7}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-14}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-x }
& = & 2 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 2 \color{blue}{+14} \\\Leftrightarrow &-4x
& = &16\\\Leftrightarrow & \color{red}{-4}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{16}{-4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)