Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-5x+3=7+x\)
- \(7x-10=13+6x\)
- \(11x-5=5-8x\)
- \(-11x+9=-1+14x\)
- \(6x+5=15-5x\)
- \(-11x-3=13+6x\)
- \(-15x+5=14+13x\)
- \(x-1=-3-x\)
- \(9x+2=14-11x\)
- \(-13x-4=-12+x\)
- \(4x-12=3-15x\)
- \(-13x+7=13+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -5x \color{red}{+3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-x }
& = & 7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 7 \color{blue}{-3} \\\Leftrightarrow &-6x
& = &4\\\Leftrightarrow & \color{red}{-6}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-10}& = & 13 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10-6x }
& = & 13 \color{red}{ +6x }\color{blue}{+10-6x } \\\Leftrightarrow & 7x \color{blue}{-6x }
& = & 13 \color{blue}{+10} \\\Leftrightarrow &x
& = &23\\\Leftrightarrow & \color{red}{}x
& = &23\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 23 \\\Leftrightarrow & \color{green}{ x = 23 } & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-5}& = & 5 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5+8x }
& = & 5 \color{red}{ -8x }\color{blue}{+5+8x } \\\Leftrightarrow & 11x \color{blue}{+8x }
& = & 5 \color{blue}{+5} \\\Leftrightarrow &19x
& = &10\\\Leftrightarrow & \color{red}{19}x
& = &10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+9}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-14x }
& = & -1 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & -11x \color{blue}{-14x }
& = & -1 \color{blue}{-9} \\\Leftrightarrow &-25x
& = &-10\\\Leftrightarrow & \color{red}{-25}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-10}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+5}& = & 15 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5+5x }
& = & 15 \color{red}{ -5x }\color{blue}{-5+5x } \\\Leftrightarrow & 6x \color{blue}{+5x }
& = & 15 \color{blue}{-5} \\\Leftrightarrow &11x
& = &10\\\Leftrightarrow & \color{red}{11}x
& = &10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-3}& = & 13 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-6x }
& = & 13 \color{red}{ +6x }\color{blue}{+3-6x } \\\Leftrightarrow & -11x \color{blue}{-6x }
& = & 13 \color{blue}{+3} \\\Leftrightarrow &-17x
& = &16\\\Leftrightarrow & \color{red}{-17}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{16}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+5}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5-13x }
& = & 14 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & 14 \color{blue}{-5} \\\Leftrightarrow &-28x
& = &9\\\Leftrightarrow & \color{red}{-28}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{9}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{28} } & & \\ & V = \left\{ \frac{-9}{28} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-1}& = & -3 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1+x }
& = & -3 \color{red}{ -x }\color{blue}{+1+x } \\\Leftrightarrow & x \color{blue}{+x }
& = & -3 \color{blue}{+1} \\\Leftrightarrow &2x
& = &-2\\\Leftrightarrow & \color{red}{2}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{-2}{2} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+2}& = & 14 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2+11x }
& = & 14 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 9x \color{blue}{+11x }
& = & 14 \color{blue}{-2} \\\Leftrightarrow &20x
& = &12\\\Leftrightarrow & \color{red}{20}x
& = &12\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{12}{20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-4}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-4}\color{blue}{+4-x }
& = & -12 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -12 \color{blue}{+4} \\\Leftrightarrow &-14x
& = &-8\\\Leftrightarrow & \color{red}{-14}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-12}& = & 3 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12+15x }
& = & 3 \color{red}{ -15x }\color{blue}{+12+15x } \\\Leftrightarrow & 4x \color{blue}{+15x }
& = & 3 \color{blue}{+12} \\\Leftrightarrow &19x
& = &15\\\Leftrightarrow & \color{red}{19}x
& = &15\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{15}{19} \\\Leftrightarrow & \color{green}{ x = \frac{15}{19} } & & \\ & V = \left\{ \frac{15}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+7}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+7}\color{blue}{-7-x }
& = & 13 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 13 \color{blue}{-7} \\\Leftrightarrow &-14x
& = &6\\\Leftrightarrow & \color{red}{-14}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)