Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(3x+3=3+14x\)
- \(12x-14=12+x\)
- \(10x-5=11+7x\)
- \(-7x+1=-8+x\)
- \(10x+6=-9+13x\)
- \(11x+5=2+7x\)
- \(-4x-4=-13+x\)
- \(8x+13=-10+x\)
- \(-5x-12=3+3x\)
- \(7x+15=-11-13x\)
- \(-6x+8=11+13x\)
- \(-13x-10=15+9x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 3x \color{red}{+3}& = & 3 \color{red}{ +14x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3-14x }
& = & 3 \color{red}{ +14x }\color{blue}{-3-14x } \\\Leftrightarrow & 3x \color{blue}{-14x }
& = & 3 \color{blue}{-3} \\\Leftrightarrow &-11x
& = &0\\\Leftrightarrow & \color{red}{-11}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-14}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14-x }
& = & 12 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & 12 \color{blue}{+14} \\\Leftrightarrow &11x
& = &26\\\Leftrightarrow & \color{red}{11}x
& = &26\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{26}{11} \\\Leftrightarrow & \color{green}{ x = \frac{26}{11} } & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-5}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-5}\color{blue}{+5-7x }
& = & 11 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & 10x \color{blue}{-7x }
& = & 11 \color{blue}{+5} \\\Leftrightarrow &3x
& = &16\\\Leftrightarrow & \color{red}{3}x
& = &16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+1}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x }
& = & -8 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -8 \color{blue}{-1} \\\Leftrightarrow &-8x
& = &-9\\\Leftrightarrow & \color{red}{-8}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+6}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6-13x }
& = & -9 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 10x \color{blue}{-13x }
& = & -9 \color{blue}{-6} \\\Leftrightarrow &-3x
& = &-15\\\Leftrightarrow & \color{red}{-3}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-15}{-3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+5}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5-7x }
& = & 2 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & 11x \color{blue}{-7x }
& = & 2 \color{blue}{-5} \\\Leftrightarrow &4x
& = &-3\\\Leftrightarrow & \color{red}{4}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{-3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-4}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-x }
& = & -13 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -13 \color{blue}{+4} \\\Leftrightarrow &-5x
& = &-9\\\Leftrightarrow & \color{red}{-5}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+13}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13-x }
& = & -10 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 8x \color{blue}{-x }
& = & -10 \color{blue}{-13} \\\Leftrightarrow &7x
& = &-23\\\Leftrightarrow & \color{red}{7}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{-23}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{7} } & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-12}& = & 3 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-3x }
& = & 3 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & -5x \color{blue}{-3x }
& = & 3 \color{blue}{+12} \\\Leftrightarrow &-8x
& = &15\\\Leftrightarrow & \color{red}{-8}x
& = &15\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{15}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+15}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+15}\color{blue}{-15+13x }
& = & -11 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 7x \color{blue}{+13x }
& = & -11 \color{blue}{-15} \\\Leftrightarrow &20x
& = &-26\\\Leftrightarrow & \color{red}{20}x
& = &-26\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{-26}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+8}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-13x }
& = & 11 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & 11 \color{blue}{-8} \\\Leftrightarrow &-19x
& = &3\\\Leftrightarrow & \color{red}{-19}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-10}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-9x }
& = & 15 \color{red}{ +9x }\color{blue}{+10-9x } \\\Leftrightarrow & -13x \color{blue}{-9x }
& = & 15 \color{blue}{+10} \\\Leftrightarrow &-22x
& = &25\\\Leftrightarrow & \color{red}{-22}x
& = &25\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}}
& = & \frac{25}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{22} } & & \\ & V = \left\{ \frac{-25}{22} \right\} & \\\end{align}\)