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