Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(13x+12=-4-6x\)
- \(7x-3=4-10x\)
- \(-15x+10=12+x\)
- \(-14x+2=13+x\)
- \(4x+6=6-7x\)
- \(-6x-8=-7+7x\)
- \(4x-9=8+3x\)
- \(3x-15=2+2x\)
- \(3x-2=-14-14x\)
- \(-10x-15=-7+x\)
- \(2x+2=12+x\)
- \(-5x+4=4+8x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 13x \color{red}{+12}& = & -4 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12+6x }
& = & -4 \color{red}{ -6x }\color{blue}{-12+6x } \\\Leftrightarrow & 13x \color{blue}{+6x }
& = & -4 \color{blue}{-12} \\\Leftrightarrow &19x
& = &-16\\\Leftrightarrow & \color{red}{19}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-16}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{19} } & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-3}& = & 4 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3+10x }
& = & 4 \color{red}{ -10x }\color{blue}{+3+10x } \\\Leftrightarrow & 7x \color{blue}{+10x }
& = & 4 \color{blue}{+3} \\\Leftrightarrow &17x
& = &7\\\Leftrightarrow & \color{red}{17}x
& = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+10}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-x }
& = & 12 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & 12 \color{blue}{-10} \\\Leftrightarrow &-16x
& = &2\\\Leftrightarrow & \color{red}{-16}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+2}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x }
& = & 13 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 13 \color{blue}{-2} \\\Leftrightarrow &-15x
& = &11\\\Leftrightarrow & \color{red}{-15}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+6}& = & 6 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6+7x }
& = & 6 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 4x \color{blue}{+7x }
& = & 6 \color{blue}{-6} \\\Leftrightarrow &11x
& = &0\\\Leftrightarrow & \color{red}{11}x
& = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-8}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-8}\color{blue}{+8-7x }
& = & -7 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & -7 \color{blue}{+8} \\\Leftrightarrow &-13x
& = &1\\\Leftrightarrow & \color{red}{-13}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-9}& = & 8 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9-3x }
& = & 8 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & 4x \color{blue}{-3x }
& = & 8 \color{blue}{+9} \\\Leftrightarrow &x
& = &17\\\Leftrightarrow & \color{red}{}x
& = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-15}& = & 2 \color{red}{ +2x } \\\Leftrightarrow & 3x \color{red}{-15}\color{blue}{+15-2x }
& = & 2 \color{red}{ +2x }\color{blue}{+15-2x } \\\Leftrightarrow & 3x \color{blue}{-2x }
& = & 2 \color{blue}{+15} \\\Leftrightarrow &x
& = &17\\\Leftrightarrow & \color{red}{}x
& = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-2}& = & -14 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2+14x }
& = & -14 \color{red}{ -14x }\color{blue}{+2+14x } \\\Leftrightarrow & 3x \color{blue}{+14x }
& = & -14 \color{blue}{+2} \\\Leftrightarrow &17x
& = &-12\\\Leftrightarrow & \color{red}{17}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{17} } & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-15}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-x }
& = & -7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -7 \color{blue}{+15} \\\Leftrightarrow &-11x
& = &8\\\Leftrightarrow & \color{red}{-11}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-x }
& = & 12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & 12 \color{blue}{-2} \\\Leftrightarrow &x
& = &10\\\Leftrightarrow & \color{red}{}x
& = &10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 10 \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+4}& = & 4 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4-8x }
& = & 4 \color{red}{ +8x }\color{blue}{-4-8x } \\\Leftrightarrow & -5x \color{blue}{-8x }
& = & 4 \color{blue}{-4} \\\Leftrightarrow &-13x
& = &0\\\Leftrightarrow & \color{red}{-13}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)