Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-x-15=11+12x\)
- \(-15x-1=15+4x\)
- \(-13x+8=2+x\)
- \(-11x-10=-7+14x\)
- \(4x-2=14-11x\)
- \(-14x-3=10+x\)
- \(2x+8=1+5x\)
- \(-2x-15=15+x\)
- \(-11x+15=1+4x\)
- \(3x+9=-7-14x\)
- \(3x-3=4-14x\)
- \(-x-2=3+4x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -x \color{red}{-15}& = & 11 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{-15}\color{blue}{+15-12x }
& = & 11 \color{red}{ +12x }\color{blue}{+15-12x } \\\Leftrightarrow & -x \color{blue}{-12x }
& = & 11 \color{blue}{+15} \\\Leftrightarrow &-13x
& = &26\\\Leftrightarrow & \color{red}{-13}x
& = &26\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{26}{-13} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-1}& = & 15 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-4x }
& = & 15 \color{red}{ +4x }\color{blue}{+1-4x } \\\Leftrightarrow & -15x \color{blue}{-4x }
& = & 15 \color{blue}{+1} \\\Leftrightarrow &-19x
& = &16\\\Leftrightarrow & \color{red}{-19}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{16}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{19} } & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+8}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-x }
& = & 2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 2 \color{blue}{-8} \\\Leftrightarrow &-14x
& = &-6\\\Leftrightarrow & \color{red}{-14}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-10}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-14x }
& = & -7 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & -11x \color{blue}{-14x }
& = & -7 \color{blue}{+10} \\\Leftrightarrow &-25x
& = &3\\\Leftrightarrow & \color{red}{-25}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{3}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{25} } & & \\ & V = \left\{ \frac{-3}{25} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-2}& = & 14 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2+11x }
& = & 14 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 4x \color{blue}{+11x }
& = & 14 \color{blue}{+2} \\\Leftrightarrow &15x
& = &16\\\Leftrightarrow & \color{red}{15}x
& = &16\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{16}{15} \\\Leftrightarrow & \color{green}{ x = \frac{16}{15} } & & \\ & V = \left\{ \frac{16}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-3}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-3}\color{blue}{+3-x }
& = & 10 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 10 \color{blue}{+3} \\\Leftrightarrow &-15x
& = &13\\\Leftrightarrow & \color{red}{-15}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+8}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-5x }
& = & 1 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & 2x \color{blue}{-5x }
& = & 1 \color{blue}{-8} \\\Leftrightarrow &-3x
& = &-7\\\Leftrightarrow & \color{red}{-3}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-15}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-x }
& = & 15 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & 15 \color{blue}{+15} \\\Leftrightarrow &-3x
& = &30\\\Leftrightarrow & \color{red}{-3}x
& = &30\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{30}{-3} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+15}& = & 1 \color{red}{ +4x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-4x }
& = & 1 \color{red}{ +4x }\color{blue}{-15-4x } \\\Leftrightarrow & -11x \color{blue}{-4x }
& = & 1 \color{blue}{-15} \\\Leftrightarrow &-15x
& = &-14\\\Leftrightarrow & \color{red}{-15}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+9}& = & -7 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9+14x }
& = & -7 \color{red}{ -14x }\color{blue}{-9+14x } \\\Leftrightarrow & 3x \color{blue}{+14x }
& = & -7 \color{blue}{-9} \\\Leftrightarrow &17x
& = &-16\\\Leftrightarrow & \color{red}{17}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-3}& = & 4 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-3}\color{blue}{+3+14x }
& = & 4 \color{red}{ -14x }\color{blue}{+3+14x } \\\Leftrightarrow & 3x \color{blue}{+14x }
& = & 4 \color{blue}{+3} \\\Leftrightarrow &17x
& = &7\\\Leftrightarrow & \color{red}{17}x
& = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-2}& = & 3 \color{red}{ +4x } \\\Leftrightarrow & -x \color{red}{-2}\color{blue}{+2-4x }
& = & 3 \color{red}{ +4x }\color{blue}{+2-4x } \\\Leftrightarrow & -x \color{blue}{-4x }
& = & 3 \color{blue}{+2} \\\Leftrightarrow &-5x
& = &5\\\Leftrightarrow & \color{red}{-5}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)