Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-9x+4=-10+x\)
- \(10x+6=15-13x\)
- \(13x+14=-1-6x\)
- \(-2x+5=13+x\)
- \(-13x-5=-7+10x\)
- \(-9x-7=-14+x\)
- \(-12x+7=-13+x\)
- \(-15x+15=-6+8x\)
- \(-11x+12=-12+x\)
- \(9x-5=15-13x\)
- \(8x-1=-13-13x\)
- \(3x-13=-11+7x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -9x \color{red}{+4}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-x }
& = & -10 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -10 \color{blue}{-4} \\\Leftrightarrow &-10x
& = &-14\\\Leftrightarrow & \color{red}{-10}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+6}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6+13x }
& = & 15 \color{red}{ -13x }\color{blue}{-6+13x } \\\Leftrightarrow & 10x \color{blue}{+13x }
& = & 15 \color{blue}{-6} \\\Leftrightarrow &23x
& = &9\\\Leftrightarrow & \color{red}{23}x
& = &9\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{9}{23} \\\Leftrightarrow & \color{green}{ x = \frac{9}{23} } & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+14}& = & -1 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14+6x }
& = & -1 \color{red}{ -6x }\color{blue}{-14+6x } \\\Leftrightarrow & 13x \color{blue}{+6x }
& = & -1 \color{blue}{-14} \\\Leftrightarrow &19x
& = &-15\\\Leftrightarrow & \color{red}{19}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-15}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{19} } & & \\ & V = \left\{ \frac{-15}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-x }
& = & 13 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & 13 \color{blue}{-5} \\\Leftrightarrow &-3x
& = &8\\\Leftrightarrow & \color{red}{-3}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-5}& = & -7 \color{red}{ +10x } \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5-10x }
& = & -7 \color{red}{ +10x }\color{blue}{+5-10x } \\\Leftrightarrow & -13x \color{blue}{-10x }
& = & -7 \color{blue}{+5} \\\Leftrightarrow &-23x
& = &-2\\\Leftrightarrow & \color{red}{-23}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{-2}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{2}{23} } & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-7}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-7}\color{blue}{+7-x }
& = & -14 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -14 \color{blue}{+7} \\\Leftrightarrow &-10x
& = &-7\\\Leftrightarrow & \color{red}{-10}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+7}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+7}\color{blue}{-7-x }
& = & -13 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -13 \color{blue}{-7} \\\Leftrightarrow &-13x
& = &-20\\\Leftrightarrow & \color{red}{-13}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+15}& = & -6 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15-8x }
& = & -6 \color{red}{ +8x }\color{blue}{-15-8x } \\\Leftrightarrow & -15x \color{blue}{-8x }
& = & -6 \color{blue}{-15} \\\Leftrightarrow &-23x
& = &-21\\\Leftrightarrow & \color{red}{-23}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{-21}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{21}{23} } & & \\ & V = \left\{ \frac{21}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+12}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-x }
& = & -12 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -12 \color{blue}{-12} \\\Leftrightarrow &-12x
& = &-24\\\Leftrightarrow & \color{red}{-12}x
& = &-24\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-24}{-12} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-5}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5+13x }
& = & 15 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 9x \color{blue}{+13x }
& = & 15 \color{blue}{+5} \\\Leftrightarrow &22x
& = &20\\\Leftrightarrow & \color{red}{22}x
& = &20\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}}
& = & \frac{20}{22} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-1}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1+13x }
& = & -13 \color{red}{ -13x }\color{blue}{+1+13x } \\\Leftrightarrow & 8x \color{blue}{+13x }
& = & -13 \color{blue}{+1} \\\Leftrightarrow &21x
& = &-12\\\Leftrightarrow & \color{red}{21}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}}
& = & \frac{-12}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-13}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13-7x }
& = & -11 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & 3x \color{blue}{-7x }
& = & -11 \color{blue}{+13} \\\Leftrightarrow &-4x
& = &2\\\Leftrightarrow & \color{red}{-4}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)