Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(11x+5=14+4x\)
- \(-10x+14=8+x\)
- \(-11x-3=-9+x\)
- \(-11x+10=3+12x\)
- \(7x+6=8+4x\)
- \(-15x-13=10+x\)
- \(-4x+14=4+x\)
- \(-13x+9=-2+14x\)
- \(13x+4=-15-6x\)
- \(-14x+1=-9+x\)
- \(9x+2=11-13x\)
- \(11x+3=-7+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 11x \color{red}{+5}& = & 14 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5-4x }
& = & 14 \color{red}{ +4x }\color{blue}{-5-4x } \\\Leftrightarrow & 11x \color{blue}{-4x }
& = & 14 \color{blue}{-5} \\\Leftrightarrow &7x
& = &9\\\Leftrightarrow & \color{red}{7}x
& = &9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+14}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-x }
& = & 8 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 8 \color{blue}{-14} \\\Leftrightarrow &-11x
& = &-6\\\Leftrightarrow & \color{red}{-11}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-3}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-x }
& = & -9 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -9 \color{blue}{+3} \\\Leftrightarrow &-12x
& = &-6\\\Leftrightarrow & \color{red}{-12}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+10}& = & 3 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-12x }
& = & 3 \color{red}{ +12x }\color{blue}{-10-12x } \\\Leftrightarrow & -11x \color{blue}{-12x }
& = & 3 \color{blue}{-10} \\\Leftrightarrow &-23x
& = &-7\\\Leftrightarrow & \color{red}{-23}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{-7}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{7}{23} } & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+6}& = & 8 \color{red}{ +4x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6-4x }
& = & 8 \color{red}{ +4x }\color{blue}{-6-4x } \\\Leftrightarrow & 7x \color{blue}{-4x }
& = & 8 \color{blue}{-6} \\\Leftrightarrow &3x
& = &2\\\Leftrightarrow & \color{red}{3}x
& = &2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13-x }
& = & 10 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & 10 \color{blue}{+13} \\\Leftrightarrow &-16x
& = &23\\\Leftrightarrow & \color{red}{-16}x
& = &23\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{23}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{16} } & & \\ & V = \left\{ \frac{-23}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14-x }
& = & 4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & 4 \color{blue}{-14} \\\Leftrightarrow &-5x
& = &-10\\\Leftrightarrow & \color{red}{-5}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-10}{-5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+9}& = & -2 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-14x }
& = & -2 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & -13x \color{blue}{-14x }
& = & -2 \color{blue}{-9} \\\Leftrightarrow &-27x
& = &-11\\\Leftrightarrow & \color{red}{-27}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}}
& = & \frac{-11}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{11}{27} } & & \\ & V = \left\{ \frac{11}{27} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+4}& = & -15 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4+6x }
& = & -15 \color{red}{ -6x }\color{blue}{-4+6x } \\\Leftrightarrow & 13x \color{blue}{+6x }
& = & -15 \color{blue}{-4} \\\Leftrightarrow &19x
& = &-19\\\Leftrightarrow & \color{red}{19}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-19}{19} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+1}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x }
& = & -9 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -9 \color{blue}{-1} \\\Leftrightarrow &-15x
& = &-10\\\Leftrightarrow & \color{red}{-15}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+2}& = & 11 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2+13x }
& = & 11 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & 9x \color{blue}{+13x }
& = & 11 \color{blue}{-2} \\\Leftrightarrow &22x
& = &9\\\Leftrightarrow & \color{red}{22}x
& = &9\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}}
& = & \frac{9}{22} \\\Leftrightarrow & \color{green}{ x = \frac{9}{22} } & & \\ & V = \left\{ \frac{9}{22} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+3}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3-x }
& = & -7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 11x \color{blue}{-x }
& = & -7 \color{blue}{-3} \\\Leftrightarrow &10x
& = &-10\\\Leftrightarrow & \color{red}{10}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{-10}{10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)