Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-15x+6=6+x\)
- \(6x+1=9+5x\)
- \(-x-1=-3-10x\)
- \(5x-7=2+12x\)
- \(-8x-5=-9+9x\)
- \(-3x-6=4+x\)
- \(4x+6=8-15x\)
- \(-12x+4=-3+13x\)
- \(6x+5=7+x\)
- \(15x+9=-4+14x\)
- \(-2x+5=-10+x\)
- \(-15x-10=-2+8x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -15x \color{red}{+6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-x }
& = & 6 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & 6 \color{blue}{-6} \\\Leftrightarrow &-16x
& = &0\\\Leftrightarrow & \color{red}{-16}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+1}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1-5x }
& = & 9 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & 6x \color{blue}{-5x }
& = & 9 \color{blue}{-1} \\\Leftrightarrow &x
& = &8\\\Leftrightarrow & \color{red}{}x
& = &8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 8 \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-1}& = & -3 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1+10x }
& = & -3 \color{red}{ -10x }\color{blue}{+1+10x } \\\Leftrightarrow & -x \color{blue}{+10x }
& = & -3 \color{blue}{+1} \\\Leftrightarrow &9x
& = &-2\\\Leftrightarrow & \color{red}{9}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-7}& = & 2 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7-12x }
& = & 2 \color{red}{ +12x }\color{blue}{+7-12x } \\\Leftrightarrow & 5x \color{blue}{-12x }
& = & 2 \color{blue}{+7} \\\Leftrightarrow &-7x
& = &9\\\Leftrightarrow & \color{red}{-7}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-5}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-9x }
& = & -9 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & -8x \color{blue}{-9x }
& = & -9 \color{blue}{+5} \\\Leftrightarrow &-17x
& = &-4\\\Leftrightarrow & \color{red}{-17}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-6}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x }
& = & 4 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 4 \color{blue}{+6} \\\Leftrightarrow &-4x
& = &10\\\Leftrightarrow & \color{red}{-4}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+6}& = & 8 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6+15x }
& = & 8 \color{red}{ -15x }\color{blue}{-6+15x } \\\Leftrightarrow & 4x \color{blue}{+15x }
& = & 8 \color{blue}{-6} \\\Leftrightarrow &19x
& = &2\\\Leftrightarrow & \color{red}{19}x
& = &2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{2}{19} } & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+4}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-13x }
& = & -3 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & -3 \color{blue}{-4} \\\Leftrightarrow &-25x
& = &-7\\\Leftrightarrow & \color{red}{-25}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-7}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{7}{25} } & & \\ & V = \left\{ \frac{7}{25} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+5}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5-x }
& = & 7 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & 7 \color{blue}{-5} \\\Leftrightarrow &5x
& = &2\\\Leftrightarrow & \color{red}{5}x
& = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+9}& = & -4 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9-14x }
& = & -4 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & 15x \color{blue}{-14x }
& = & -4 \color{blue}{-9} \\\Leftrightarrow &x
& = &-13\\\Leftrightarrow & \color{red}{}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -13 \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+5}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-x }
& = & -10 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & -10 \color{blue}{-5} \\\Leftrightarrow &-3x
& = &-15\\\Leftrightarrow & \color{red}{-3}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-15}{-3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-10}& = & -2 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-8x }
& = & -2 \color{red}{ +8x }\color{blue}{+10-8x } \\\Leftrightarrow & -15x \color{blue}{-8x }
& = & -2 \color{blue}{+10} \\\Leftrightarrow &-23x
& = &8\\\Leftrightarrow & \color{red}{-23}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{8}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{23} } & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)