Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(4x+11=-15-11x\)
- \(6x-10=3+x\)
- \(x+9=-8+8x\)
- \(-x+6=8+15x\)
- \(2x-3=1+9x\)
- \(13x-10=7-6x\)
- \(x+13=-10+7x\)
- \(-x+7=-11+5x\)
- \(-6x+12=-4+x\)
- \(-6x-2=15+x\)
- \(4x-14=-14+9x\)
- \(-3x-11=14+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 4x \color{red}{+11}& = & -15 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11+11x }
& = & -15 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 4x \color{blue}{+11x }
& = & -15 \color{blue}{-11} \\\Leftrightarrow &15x
& = &-26\\\Leftrightarrow & \color{red}{15}x
& = &-26\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{-26}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{15} } & & \\ & V = \left\{ \frac{-26}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10-x }
& = & 3 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & 3 \color{blue}{+10} \\\Leftrightarrow &5x
& = &13\\\Leftrightarrow & \color{red}{5}x
& = &13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+9}& = & -8 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9-8x }
& = & -8 \color{red}{ +8x }\color{blue}{-9-8x } \\\Leftrightarrow & x \color{blue}{-8x }
& = & -8 \color{blue}{-9} \\\Leftrightarrow &-7x
& = &-17\\\Leftrightarrow & \color{red}{-7}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+6}& = & 8 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6-15x }
& = & 8 \color{red}{ +15x }\color{blue}{-6-15x } \\\Leftrightarrow & -x \color{blue}{-15x }
& = & 8 \color{blue}{-6} \\\Leftrightarrow &-16x
& = &2\\\Leftrightarrow & \color{red}{-16}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-3}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-9x }
& = & 1 \color{red}{ +9x }\color{blue}{+3-9x } \\\Leftrightarrow & 2x \color{blue}{-9x }
& = & 1 \color{blue}{+3} \\\Leftrightarrow &-7x
& = &4\\\Leftrightarrow & \color{red}{-7}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-10}& = & 7 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10+6x }
& = & 7 \color{red}{ -6x }\color{blue}{+10+6x } \\\Leftrightarrow & 13x \color{blue}{+6x }
& = & 7 \color{blue}{+10} \\\Leftrightarrow &19x
& = &17\\\Leftrightarrow & \color{red}{19}x
& = &17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{17}{19} } & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+13}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13-7x }
& = & -10 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & x \color{blue}{-7x }
& = & -10 \color{blue}{-13} \\\Leftrightarrow &-6x
& = &-23\\\Leftrightarrow & \color{red}{-6}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-23}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{23}{6} } & & \\ & V = \left\{ \frac{23}{6} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+7}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7-5x }
& = & -11 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & -x \color{blue}{-5x }
& = & -11 \color{blue}{-7} \\\Leftrightarrow &-6x
& = &-18\\\Leftrightarrow & \color{red}{-6}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-18}{-6} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+12}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12-x }
& = & -4 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -4 \color{blue}{-12} \\\Leftrightarrow &-7x
& = &-16\\\Leftrightarrow & \color{red}{-7}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-x }
& = & 15 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & 15 \color{blue}{+2} \\\Leftrightarrow &-7x
& = &17\\\Leftrightarrow & \color{red}{-7}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-14}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14-9x }
& = & -14 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & 4x \color{blue}{-9x }
& = & -14 \color{blue}{+14} \\\Leftrightarrow &-5x
& = &0\\\Leftrightarrow & \color{red}{-5}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-11}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-x }
& = & 14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 14 \color{blue}{+11} \\\Leftrightarrow &-4x
& = &25\\\Leftrightarrow & \color{red}{-4}x
& = &25\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{25}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{4} } & & \\ & V = \left\{ \frac{-25}{4} \right\} & \\\end{align}\)