Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(8x+5=3+13x\)
- \(6x-7=-10-11x\)
- \(-13x-15=15+x\)
- \(-6x+9=-4+7x\)
- \(6x+2=11+x\)
- \(-4x+15=8+x\)
- \(-6x-9=-10+13x\)
- \(-2x-13=-7+x\)
- \(-2x-12=-6+3x\)
- \(14x-2=-9+3x\)
- \(-3x-2=-7+13x\)
- \(-6x+9=6+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 8x \color{red}{+5}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5-13x }
& = & 3 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 8x \color{blue}{-13x }
& = & 3 \color{blue}{-5} \\\Leftrightarrow &-5x
& = &-2\\\Leftrightarrow & \color{red}{-5}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-7}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7+11x }
& = & -10 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & -10 \color{blue}{+7} \\\Leftrightarrow &17x
& = &-3\\\Leftrightarrow & \color{red}{17}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-15}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-x }
& = & 15 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 15 \color{blue}{+15} \\\Leftrightarrow &-14x
& = &30\\\Leftrightarrow & \color{red}{-14}x
& = &30\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{30}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+9}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-7x }
& = & -4 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & -4 \color{blue}{-9} \\\Leftrightarrow &-13x
& = &-13\\\Leftrightarrow & \color{red}{-13}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+2}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2-x }
& = & 11 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & 11 \color{blue}{-2} \\\Leftrightarrow &5x
& = &9\\\Leftrightarrow & \color{red}{5}x
& = &9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+15}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15-x }
& = & 8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & 8 \color{blue}{-15} \\\Leftrightarrow &-5x
& = &-7\\\Leftrightarrow & \color{red}{-5}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-9}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-13x }
& = & -10 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & -10 \color{blue}{+9} \\\Leftrightarrow &-19x
& = &-1\\\Leftrightarrow & \color{red}{-19}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-13}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-13}\color{blue}{+13-x }
& = & -7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & -7 \color{blue}{+13} \\\Leftrightarrow &-3x
& = &6\\\Leftrightarrow & \color{red}{-3}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{6}{-3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-12}& = & -6 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-3x }
& = & -6 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & -2x \color{blue}{-3x }
& = & -6 \color{blue}{+12} \\\Leftrightarrow &-5x
& = &6\\\Leftrightarrow & \color{red}{-5}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-2}& = & -9 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2-3x }
& = & -9 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & 14x \color{blue}{-3x }
& = & -9 \color{blue}{+2} \\\Leftrightarrow &11x
& = &-7\\\Leftrightarrow & \color{red}{11}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-2}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2-13x }
& = & -7 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -3x \color{blue}{-13x }
& = & -7 \color{blue}{+2} \\\Leftrightarrow &-16x
& = &-5\\\Leftrightarrow & \color{red}{-16}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{16} } & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+9}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-x }
& = & 6 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & 6 \color{blue}{-9} \\\Leftrightarrow &-7x
& = &-3\\\Leftrightarrow & \color{red}{-7}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)