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