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