Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-11x-1=-10+12x\)
- \(-9x+15=13+x\)
- \(-6x-4=5+13x\)
- \(14x+1=-15-11x\)
- \(-4x+4=-14+x\)
- \(-7x+4=-14+8x\)
- \(7x-2=4+x\)
- \(-13x+9=-6+x\)
- \(-6x+6=4+x\)
- \(11x+2=-7+4x\)
- \(3x-3=-10+13x\)
- \(-6x+10=-13+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -11x \color{red}{-1}& = & -10 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-12x }
& = & -10 \color{red}{ +12x }\color{blue}{+1-12x } \\\Leftrightarrow & -11x \color{blue}{-12x }
& = & -10 \color{blue}{+1} \\\Leftrightarrow &-23x
& = &-9\\\Leftrightarrow & \color{red}{-23}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{-9}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{9}{23} } & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+15}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-x }
& = & 13 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 13 \color{blue}{-15} \\\Leftrightarrow &-10x
& = &-2\\\Leftrightarrow & \color{red}{-10}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-4}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-4}\color{blue}{+4-13x }
& = & 5 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & 5 \color{blue}{+4} \\\Leftrightarrow &-19x
& = &9\\\Leftrightarrow & \color{red}{-19}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+1}& = & -15 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1+11x }
& = & -15 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & 14x \color{blue}{+11x }
& = & -15 \color{blue}{-1} \\\Leftrightarrow &25x
& = &-16\\\Leftrightarrow & \color{red}{25}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}}
& = & \frac{-16}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{25} } & & \\ & V = \left\{ \frac{-16}{25} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+4}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x }
& = & -14 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -14 \color{blue}{-4} \\\Leftrightarrow &-5x
& = &-18\\\Leftrightarrow & \color{red}{-5}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+4}& = & -14 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-8x }
& = & -14 \color{red}{ +8x }\color{blue}{-4-8x } \\\Leftrightarrow & -7x \color{blue}{-8x }
& = & -14 \color{blue}{-4} \\\Leftrightarrow &-15x
& = &-18\\\Leftrightarrow & \color{red}{-15}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2-x }
& = & 4 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 7x \color{blue}{-x }
& = & 4 \color{blue}{+2} \\\Leftrightarrow &6x
& = &6\\\Leftrightarrow & \color{red}{6}x
& = &6\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}}
& = & \frac{6}{6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+9}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-x }
& = & -6 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -6 \color{blue}{-9} \\\Leftrightarrow &-14x
& = &-15\\\Leftrightarrow & \color{red}{-14}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{14} } & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+6}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6-x }
& = & 4 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & 4 \color{blue}{-6} \\\Leftrightarrow &-7x
& = &-2\\\Leftrightarrow & \color{red}{-7}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+2}& = & -7 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2-4x }
& = & -7 \color{red}{ +4x }\color{blue}{-2-4x } \\\Leftrightarrow & 11x \color{blue}{-4x }
& = & -7 \color{blue}{-2} \\\Leftrightarrow &7x
& = &-9\\\Leftrightarrow & \color{red}{7}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{-9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-3}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{-3}\color{blue}{+3-13x }
& = & -10 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & 3x \color{blue}{-13x }
& = & -10 \color{blue}{+3} \\\Leftrightarrow &-10x
& = &-7\\\Leftrightarrow & \color{red}{-10}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10-x }
& = & -13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -13 \color{blue}{-10} \\\Leftrightarrow &-7x
& = &-23\\\Leftrightarrow & \color{red}{-7}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-23}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)