Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(6x-4=13+x\)
- \(7x-11=-8+3x\)
- \(-4x-5=2+x\)
- \(-14x+15=-15+x\)
- \(7x-9=6-2x\)
- \(-8x-11=-1+9x\)
- \(10x-3=9-13x\)
- \(-10x-10=6+x\)
- \(15x+6=8+8x\)
- \(-4x-11=7+x\)
- \(6x+8=4-11x\)
- \(-11x-13=6+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 6x \color{red}{-4}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4-x }
& = & 13 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & 13 \color{blue}{+4} \\\Leftrightarrow &5x
& = &17\\\Leftrightarrow & \color{red}{5}x
& = &17\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{17}{5} \\\Leftrightarrow & \color{green}{ x = \frac{17}{5} } & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-11}& = & -8 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11-3x }
& = & -8 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & 7x \color{blue}{-3x }
& = & -8 \color{blue}{+11} \\\Leftrightarrow &4x
& = &3\\\Leftrightarrow & \color{red}{4}x
& = &3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-x }
& = & 2 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & 2 \color{blue}{+5} \\\Leftrightarrow &-5x
& = &7\\\Leftrightarrow & \color{red}{-5}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+15}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15-x }
& = & -15 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -15 \color{blue}{-15} \\\Leftrightarrow &-15x
& = &-30\\\Leftrightarrow & \color{red}{-15}x
& = &-30\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-30}{-15} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-9}& = & 6 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9+2x }
& = & 6 \color{red}{ -2x }\color{blue}{+9+2x } \\\Leftrightarrow & 7x \color{blue}{+2x }
& = & 6 \color{blue}{+9} \\\Leftrightarrow &9x
& = &15\\\Leftrightarrow & \color{red}{9}x
& = &15\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{15}{9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-11}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-9x }
& = & -1 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & -8x \color{blue}{-9x }
& = & -1 \color{blue}{+11} \\\Leftrightarrow &-17x
& = &10\\\Leftrightarrow & \color{red}{-17}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-3}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3+13x }
& = & 9 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 10x \color{blue}{+13x }
& = & 9 \color{blue}{+3} \\\Leftrightarrow &23x
& = &12\\\Leftrightarrow & \color{red}{23}x
& = &12\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{12}{23} \\\Leftrightarrow & \color{green}{ x = \frac{12}{23} } & & \\ & V = \left\{ \frac{12}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-10}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x }
& = & 6 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 6 \color{blue}{+10} \\\Leftrightarrow &-11x
& = &16\\\Leftrightarrow & \color{red}{-11}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+6}& = & 8 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6-8x }
& = & 8 \color{red}{ +8x }\color{blue}{-6-8x } \\\Leftrightarrow & 15x \color{blue}{-8x }
& = & 8 \color{blue}{-6} \\\Leftrightarrow &7x
& = &2\\\Leftrightarrow & \color{red}{7}x
& = &2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-11}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-x }
& = & 7 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & 7 \color{blue}{+11} \\\Leftrightarrow &-5x
& = &18\\\Leftrightarrow & \color{red}{-5}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+8}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8+11x }
& = & 4 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & 4 \color{blue}{-8} \\\Leftrightarrow &17x
& = &-4\\\Leftrightarrow & \color{red}{17}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-13}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-x }
& = & 6 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 6 \color{blue}{+13} \\\Leftrightarrow &-12x
& = &19\\\Leftrightarrow & \color{red}{-12}x
& = &19\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{19}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{12} } & & \\ & V = \left\{ \frac{-19}{12} \right\} & \\\end{align}\)