Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(14x-15=-2-9x\)
- \(-6x-13=-7+7x\)
- \(-12x-10=-7+x\)
- \(9x+15=7+14x\)
- \(-15x-12=-3+13x\)
- \(3x+15=-13-8x\)
- \(-13x+4=4+x\)
- \(8x-2=11-5x\)
- \(4x-7=-1-11x\)
- \(-5x-1=-6+11x\)
- \(-6x-13=-1+13x\)
- \(6x+11=11+13x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 14x \color{red}{-15}& = & -2 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15+9x }
& = & -2 \color{red}{ -9x }\color{blue}{+15+9x } \\\Leftrightarrow & 14x \color{blue}{+9x }
& = & -2 \color{blue}{+15} \\\Leftrightarrow &23x
& = &13\\\Leftrightarrow & \color{red}{23}x
& = &13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{13}{23} } & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-13}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-7x }
& = & -7 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & -7 \color{blue}{+13} \\\Leftrightarrow &-13x
& = &6\\\Leftrightarrow & \color{red}{-13}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-10}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-x }
& = & -7 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -7 \color{blue}{+10} \\\Leftrightarrow &-13x
& = &3\\\Leftrightarrow & \color{red}{-13}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+15}& = & 7 \color{red}{ +14x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15-14x }
& = & 7 \color{red}{ +14x }\color{blue}{-15-14x } \\\Leftrightarrow & 9x \color{blue}{-14x }
& = & 7 \color{blue}{-15} \\\Leftrightarrow &-5x
& = &-8\\\Leftrightarrow & \color{red}{-5}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-12}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-13x }
& = & -3 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & -3 \color{blue}{+12} \\\Leftrightarrow &-28x
& = &9\\\Leftrightarrow & \color{red}{-28}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{9}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{28} } & & \\ & V = \left\{ \frac{-9}{28} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+15}& = & -13 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+15}\color{blue}{-15+8x }
& = & -13 \color{red}{ -8x }\color{blue}{-15+8x } \\\Leftrightarrow & 3x \color{blue}{+8x }
& = & -13 \color{blue}{-15} \\\Leftrightarrow &11x
& = &-28\\\Leftrightarrow & \color{red}{11}x
& = &-28\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-28}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{11} } & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+4}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x }
& = & 4 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 4 \color{blue}{-4} \\\Leftrightarrow &-14x
& = &0\\\Leftrightarrow & \color{red}{-14}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-2}& = & 11 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2+5x }
& = & 11 \color{red}{ -5x }\color{blue}{+2+5x } \\\Leftrightarrow & 8x \color{blue}{+5x }
& = & 11 \color{blue}{+2} \\\Leftrightarrow &13x
& = &13\\\Leftrightarrow & \color{red}{13}x
& = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-7}& = & -1 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-7}\color{blue}{+7+11x }
& = & -1 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 4x \color{blue}{+11x }
& = & -1 \color{blue}{+7} \\\Leftrightarrow &15x
& = &6\\\Leftrightarrow & \color{red}{15}x
& = &6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-1}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-11x }
& = & -6 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & -5x \color{blue}{-11x }
& = & -6 \color{blue}{+1} \\\Leftrightarrow &-16x
& = &-5\\\Leftrightarrow & \color{red}{-16}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{16} } & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-13}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-13x }
& = & -1 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & -1 \color{blue}{+13} \\\Leftrightarrow &-19x
& = &12\\\Leftrightarrow & \color{red}{-19}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{12}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{19} } & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+11}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11-13x }
& = & 11 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & 6x \color{blue}{-13x }
& = & 11 \color{blue}{-11} \\\Leftrightarrow &-7x
& = &0\\\Leftrightarrow & \color{red}{-7}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)