Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(8x-4=5-7x\)
- \(15x-11=13-14x\)
- \(-6x+9=-4+x\)
- \(-7x+4=1+4x\)
- \(14x-8=-13-9x\)
- \(-3x-3=-11+x\)
- \(-11x-10=14+x\)
- \(-15x+1=6+x\)
- \(-4x-15=14+13x\)
- \(13x+9=-2+12x\)
- \(13x-9=4-6x\)
- \(7x-3=6+2x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 8x \color{red}{-4}& = & 5 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4+7x }
& = & 5 \color{red}{ -7x }\color{blue}{+4+7x } \\\Leftrightarrow & 8x \color{blue}{+7x }
& = & 5 \color{blue}{+4} \\\Leftrightarrow &15x
& = &9\\\Leftrightarrow & \color{red}{15}x
& = &9\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{9}{15} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-11}& = & 13 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11+14x }
& = & 13 \color{red}{ -14x }\color{blue}{+11+14x } \\\Leftrightarrow & 15x \color{blue}{+14x }
& = & 13 \color{blue}{+11} \\\Leftrightarrow &29x
& = &24\\\Leftrightarrow & \color{red}{29}x
& = &24\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}}
& = & \frac{24}{29} \\\Leftrightarrow & \color{green}{ x = \frac{24}{29} } & & \\ & V = \left\{ \frac{24}{29} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+9}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-x }
& = & -4 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -4 \color{blue}{-9} \\\Leftrightarrow &-7x
& = &-13\\\Leftrightarrow & \color{red}{-7}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+4}& = & 1 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-4x }
& = & 1 \color{red}{ +4x }\color{blue}{-4-4x } \\\Leftrightarrow & -7x \color{blue}{-4x }
& = & 1 \color{blue}{-4} \\\Leftrightarrow &-11x
& = &-3\\\Leftrightarrow & \color{red}{-11}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-8}& = & -13 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8+9x }
& = & -13 \color{red}{ -9x }\color{blue}{+8+9x } \\\Leftrightarrow & 14x \color{blue}{+9x }
& = & -13 \color{blue}{+8} \\\Leftrightarrow &23x
& = &-5\\\Leftrightarrow & \color{red}{23}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-5}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{23} } & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-x }
& = & -11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -11 \color{blue}{+3} \\\Leftrightarrow &-4x
& = &-8\\\Leftrightarrow & \color{red}{-4}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-8}{-4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-10}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-x }
& = & 14 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 14 \color{blue}{+10} \\\Leftrightarrow &-12x
& = &24\\\Leftrightarrow & \color{red}{-12}x
& = &24\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{24}{-12} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+1}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-x }
& = & 6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & 6 \color{blue}{-1} \\\Leftrightarrow &-16x
& = &5\\\Leftrightarrow & \color{red}{-16}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{16} } & & \\ & V = \left\{ \frac{-5}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-15}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-13x }
& = & 14 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -4x \color{blue}{-13x }
& = & 14 \color{blue}{+15} \\\Leftrightarrow &-17x
& = &29\\\Leftrightarrow & \color{red}{-17}x
& = &29\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{29}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{17} } & & \\ & V = \left\{ \frac{-29}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+9}& = & -2 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9-12x }
& = & -2 \color{red}{ +12x }\color{blue}{-9-12x } \\\Leftrightarrow & 13x \color{blue}{-12x }
& = & -2 \color{blue}{-9} \\\Leftrightarrow &x
& = &-11\\\Leftrightarrow & \color{red}{}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-9}& = & 4 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-9}\color{blue}{+9+6x }
& = & 4 \color{red}{ -6x }\color{blue}{+9+6x } \\\Leftrightarrow & 13x \color{blue}{+6x }
& = & 4 \color{blue}{+9} \\\Leftrightarrow &19x
& = &13\\\Leftrightarrow & \color{red}{19}x
& = &13\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{13}{19} \\\Leftrightarrow & \color{green}{ x = \frac{13}{19} } & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-3}& = & 6 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3-2x }
& = & 6 \color{red}{ +2x }\color{blue}{+3-2x } \\\Leftrightarrow & 7x \color{blue}{-2x }
& = & 6 \color{blue}{+3} \\\Leftrightarrow &5x
& = &9\\\Leftrightarrow & \color{red}{5}x
& = &9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)