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