Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(11x-13=14-5x\)
- \(11x+15=-3+x\)
- \(10x-2=7-13x\)
- \(13x+3=8+x\)
- \(-11x+6=10+x\)
- \(-10x+2=-1+x\)
- \(-5x+15=9+11x\)
- \(2x+14=-15+7x\)
- \(-3x-9=-7+x\)
- \(-2x+14=-6+5x\)
- \(7x+12=13-3x\)
- \(3x-15=1-8x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 11x \color{red}{-13}& = & 14 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13+5x }
& = & 14 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 11x \color{blue}{+5x }
& = & 14 \color{blue}{+13} \\\Leftrightarrow &16x
& = &27\\\Leftrightarrow & \color{red}{16}x
& = &27\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}}
& = & \frac{27}{16} \\\Leftrightarrow & \color{green}{ x = \frac{27}{16} } & & \\ & V = \left\{ \frac{27}{16} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+15}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15-x }
& = & -3 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 11x \color{blue}{-x }
& = & -3 \color{blue}{-15} \\\Leftrightarrow &10x
& = &-18\\\Leftrightarrow & \color{red}{10}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{-18}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-2}& = & 7 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2+13x }
& = & 7 \color{red}{ -13x }\color{blue}{+2+13x } \\\Leftrightarrow & 10x \color{blue}{+13x }
& = & 7 \color{blue}{+2} \\\Leftrightarrow &23x
& = &9\\\Leftrightarrow & \color{red}{23}x
& = &9\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{9}{23} \\\Leftrightarrow & \color{green}{ x = \frac{9}{23} } & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+3}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3-x }
& = & 8 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 13x \color{blue}{-x }
& = & 8 \color{blue}{-3} \\\Leftrightarrow &12x
& = &5\\\Leftrightarrow & \color{red}{12}x
& = &5\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}}
& = & \frac{5}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6-x }
& = & 10 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 10 \color{blue}{-6} \\\Leftrightarrow &-12x
& = &4\\\Leftrightarrow & \color{red}{-12}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+2}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-x }
& = & -1 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -1 \color{blue}{-2} \\\Leftrightarrow &-11x
& = &-3\\\Leftrightarrow & \color{red}{-11}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+15}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15-11x }
& = & 9 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & -5x \color{blue}{-11x }
& = & 9 \color{blue}{-15} \\\Leftrightarrow &-16x
& = &-6\\\Leftrightarrow & \color{red}{-16}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+14}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-7x }
& = & -15 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & 2x \color{blue}{-7x }
& = & -15 \color{blue}{-14} \\\Leftrightarrow &-5x
& = &-29\\\Leftrightarrow & \color{red}{-5}x
& = &-29\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-29}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{29}{5} } & & \\ & V = \left\{ \frac{29}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-9}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-x }
& = & -7 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -7 \color{blue}{+9} \\\Leftrightarrow &-4x
& = &2\\\Leftrightarrow & \color{red}{-4}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+14}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-5x }
& = & -6 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & -2x \color{blue}{-5x }
& = & -6 \color{blue}{-14} \\\Leftrightarrow &-7x
& = &-20\\\Leftrightarrow & \color{red}{-7}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-20}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{20}{7} } & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+12}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12+3x }
& = & 13 \color{red}{ -3x }\color{blue}{-12+3x } \\\Leftrightarrow & 7x \color{blue}{+3x }
& = & 13 \color{blue}{-12} \\\Leftrightarrow &10x
& = &1\\\Leftrightarrow & \color{red}{10}x
& = &1\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{1}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-15}& = & 1 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-15}\color{blue}{+15+8x }
& = & 1 \color{red}{ -8x }\color{blue}{+15+8x } \\\Leftrightarrow & 3x \color{blue}{+8x }
& = & 1 \color{blue}{+15} \\\Leftrightarrow &11x
& = &16\\\Leftrightarrow & \color{red}{11}x
& = &16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)