Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-13x+2=-11+x\)
2. \(3x-4=8-14x\)
3. \(x+9=6+4x\)
4. \(3x+13=9+4x\)
5. \(-x-15=-4+2x\)
6. \(6x-10=8+x\)
7. \(11x-8=-14+6x\)
8. \(-11x+11=6+x\)
9. \(14x+4=-7+9x\)
10. \(-9x-14=-1+14x\)
11. \(5x-3=-9-7x\)
12. \(-8x+8=-2+x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+2}\color{blue}{-2-x } & = & -11 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -11 \color{blue}{-2} \\\Leftrightarrow &-14x & = &-13\\\Leftrightarrow & \color{red}{-14}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-13}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{14} } & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-4}& = & 8 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4+14x } & = & 8 \color{red}{ -14x }\color{blue}{+4+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &17x & = &12\\\Leftrightarrow & \color{red}{17}x & = &12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+9}& = & 6 \color{red}{ +4x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9-4x } & = & 6 \color{red}{ +4x }\color{blue}{-9-4x } \\\Leftrightarrow & x \color{blue}{-4x } & = & 6 \color{blue}{-9} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+13}& = & 9 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13-4x } & = & 9 \color{red}{ +4x }\color{blue}{-13-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 9 \color{blue}{-13} \\\Leftrightarrow &-x & = &-4\\\Leftrightarrow & \color{red}{-}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-4}{-1} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-15}& = & -4 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{-15}\color{blue}{+15-2x } & = & -4 \color{red}{ +2x }\color{blue}{+15-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & -4 \color{blue}{+15} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-10}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10-x } & = & 8 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 8 \color{blue}{+10} \\\Leftrightarrow &5x & = &18\\\Leftrightarrow & \color{red}{5}x & = &18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-8}& = & -14 \color{red}{ +6x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8-6x } & = & -14 \color{red}{ +6x }\color{blue}{+8-6x } \\\Leftrightarrow & 11x \color{blue}{-6x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &5x & = &-6\\\Leftrightarrow & \color{red}{5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+11}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+11}\color{blue}{-11-x } & = & 6 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 6 \color{blue}{-11} \\\Leftrightarrow &-12x & = &-5\\\Leftrightarrow & \color{red}{-12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+4}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4-9x } & = & -7 \color{red}{ +9x }\color{blue}{-4-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &5x & = &-11\\\Leftrightarrow & \color{red}{5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-14}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-14x } & = & -1 \color{red}{ +14x }\color{blue}{+14-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &-23x & = &13\\\Leftrightarrow & \color{red}{-23}x & = &13\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{13}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{23} } & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-3}& = & -9 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3+7x } & = & -9 \color{red}{ -7x }\color{blue}{+3+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &12x & = &-6\\\Leftrightarrow & \color{red}{12}x & = &-6\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-6}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-x } & = & -2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &-9x & = &-10\\\Leftrightarrow & \color{red}{-9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)