Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-4x+3=-12+x\)
- \(-7x-2=15+x\)
- \(13x-3=-1-6x\)
- \(13x-3=10-15x\)
- \(15x-7=-8+11x\)
- \(-11x+13=13+6x\)
- \(15x+8=-4-2x\)
- \(-4x+8=8+x\)
- \(14x-11=13+5x\)
- \(-9x-1=-9+5x\)
- \(13x-7=-14-6x\)
- \(12x+4=-1+11x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -4x \color{red}{+3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3-x }
& = & -12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -12 \color{blue}{-3} \\\Leftrightarrow &-5x
& = &-15\\\Leftrightarrow & \color{red}{-5}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-15}{-5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x }
& = & 15 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & 15 \color{blue}{+2} \\\Leftrightarrow &-8x
& = &17\\\Leftrightarrow & \color{red}{-8}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{8} } & & \\ & V = \left\{ \frac{-17}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-3}& = & -1 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3+6x }
& = & -1 \color{red}{ -6x }\color{blue}{+3+6x } \\\Leftrightarrow & 13x \color{blue}{+6x }
& = & -1 \color{blue}{+3} \\\Leftrightarrow &19x
& = &2\\\Leftrightarrow & \color{red}{19}x
& = &2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{2}{19} } & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-3}& = & 10 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3+15x }
& = & 10 \color{red}{ -15x }\color{blue}{+3+15x } \\\Leftrightarrow & 13x \color{blue}{+15x }
& = & 10 \color{blue}{+3} \\\Leftrightarrow &28x
& = &13\\\Leftrightarrow & \color{red}{28}x
& = &13\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}}
& = & \frac{13}{28} \\\Leftrightarrow & \color{green}{ x = \frac{13}{28} } & & \\ & V = \left\{ \frac{13}{28} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-7}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-7}\color{blue}{+7-11x }
& = & -8 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & 15x \color{blue}{-11x }
& = & -8 \color{blue}{+7} \\\Leftrightarrow &4x
& = &-1\\\Leftrightarrow & \color{red}{4}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{-1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+13}& = & 13 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13-6x }
& = & 13 \color{red}{ +6x }\color{blue}{-13-6x } \\\Leftrightarrow & -11x \color{blue}{-6x }
& = & 13 \color{blue}{-13} \\\Leftrightarrow &-17x
& = &0\\\Leftrightarrow & \color{red}{-17}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{0}{-17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+8}& = & -4 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+8}\color{blue}{-8+2x }
& = & -4 \color{red}{ -2x }\color{blue}{-8+2x } \\\Leftrightarrow & 15x \color{blue}{+2x }
& = & -4 \color{blue}{-8} \\\Leftrightarrow &17x
& = &-12\\\Leftrightarrow & \color{red}{17}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{17} } & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+8}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8-x }
& = & 8 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & 8 \color{blue}{-8} \\\Leftrightarrow &-5x
& = &0\\\Leftrightarrow & \color{red}{-5}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-11}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11-5x }
& = & 13 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & 14x \color{blue}{-5x }
& = & 13 \color{blue}{+11} \\\Leftrightarrow &9x
& = &24\\\Leftrightarrow & \color{red}{9}x
& = &24\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{24}{9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-1}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-1}\color{blue}{+1-5x }
& = & -9 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & -9x \color{blue}{-5x }
& = & -9 \color{blue}{+1} \\\Leftrightarrow &-14x
& = &-8\\\Leftrightarrow & \color{red}{-14}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-7}& = & -14 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7+6x }
& = & -14 \color{red}{ -6x }\color{blue}{+7+6x } \\\Leftrightarrow & 13x \color{blue}{+6x }
& = & -14 \color{blue}{+7} \\\Leftrightarrow &19x
& = &-7\\\Leftrightarrow & \color{red}{19}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{19} } & & \\ & V = \left\{ \frac{-7}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+4}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4-11x }
& = & -1 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 12x \color{blue}{-11x }
& = & -1 \color{blue}{-4} \\\Leftrightarrow &x
& = &-5\\\Leftrightarrow & \color{red}{}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)