Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(3x-4=8+x\)
- \(-13x+9=-5+7x\)
- \(x-1=-5-8x\)
- \(7x+10=-2+6x\)
- \(-13x+4=4+x\)
- \(x-15=-10-9x\)
- \(-6x+3=7+x\)
- \(-12x+15=-6+x\)
- \(-11x+6=-15+x\)
- \(4x+2=-6-11x\)
- \(-15x+11=-3+x\)
- \(15x+4=-2-2x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 3x \color{red}{-4}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4-x }
& = & 8 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 3x \color{blue}{-x }
& = & 8 \color{blue}{+4} \\\Leftrightarrow &2x
& = &12\\\Leftrightarrow & \color{red}{2}x
& = &12\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{12}{2} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+9}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-7x }
& = & -5 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & -13x \color{blue}{-7x }
& = & -5 \color{blue}{-9} \\\Leftrightarrow &-20x
& = &-14\\\Leftrightarrow & \color{red}{-20}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}}
& = & \frac{-14}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-1}& = & -5 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1+8x }
& = & -5 \color{red}{ -8x }\color{blue}{+1+8x } \\\Leftrightarrow & x \color{blue}{+8x }
& = & -5 \color{blue}{+1} \\\Leftrightarrow &9x
& = &-4\\\Leftrightarrow & \color{red}{9}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+10}& = & -2 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10-6x }
& = & -2 \color{red}{ +6x }\color{blue}{-10-6x } \\\Leftrightarrow & 7x \color{blue}{-6x }
& = & -2 \color{blue}{-10} \\\Leftrightarrow &x
& = &-12\\\Leftrightarrow & \color{red}{}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+4}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x }
& = & 4 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 4 \color{blue}{-4} \\\Leftrightarrow &-14x
& = &0\\\Leftrightarrow & \color{red}{-14}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-15}& = & -10 \color{red}{ -9x } \\\Leftrightarrow & x \color{red}{-15}\color{blue}{+15+9x }
& = & -10 \color{red}{ -9x }\color{blue}{+15+9x } \\\Leftrightarrow & x \color{blue}{+9x }
& = & -10 \color{blue}{+15} \\\Leftrightarrow &10x
& = &5\\\Leftrightarrow & \color{red}{10}x
& = &5\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{5}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-x }
& = & 7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & 7 \color{blue}{-3} \\\Leftrightarrow &-7x
& = &4\\\Leftrightarrow & \color{red}{-7}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-x }
& = & -6 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -6 \color{blue}{-15} \\\Leftrightarrow &-13x
& = &-21\\\Leftrightarrow & \color{red}{-13}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-21}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{21}{13} } & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+6}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6-x }
& = & -15 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -15 \color{blue}{-6} \\\Leftrightarrow &-12x
& = &-21\\\Leftrightarrow & \color{red}{-12}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-21}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+2}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2+11x }
& = & -6 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 4x \color{blue}{+11x }
& = & -6 \color{blue}{-2} \\\Leftrightarrow &15x
& = &-8\\\Leftrightarrow & \color{red}{15}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{-8}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+11}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-x }
& = & -3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & -3 \color{blue}{-11} \\\Leftrightarrow &-16x
& = &-14\\\Leftrightarrow & \color{red}{-16}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+4}& = & -2 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4+2x }
& = & -2 \color{red}{ -2x }\color{blue}{-4+2x } \\\Leftrightarrow & 15x \color{blue}{+2x }
& = & -2 \color{blue}{-4} \\\Leftrightarrow &17x
& = &-6\\\Leftrightarrow & \color{red}{17}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-6}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)