Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-13}& = & 10 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13-10x } & = & 10 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &-13x & = &23\\\Leftrightarrow & \color{red}{-13}x & = &23\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{23}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{13} } & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+14}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14-x } & = & -1 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-15\\\Leftrightarrow & \color{red}{-5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-15}{-5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+14}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14-x } & = & -10 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -10 \color{blue}{-14} \\\Leftrightarrow &2x & = &-24\\\Leftrightarrow & \color{red}{2}x & = &-24\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-24}{2} \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9-x } & = & 13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &4x & = &22\\\Leftrightarrow & \color{red}{4}x & = &22\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{22}{4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-2}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2-4x } & = & 13 \color{red}{ +4x }\color{blue}{+2-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 13 \color{blue}{+2} \\\Leftrightarrow &11x & = &15\\\Leftrightarrow & \color{red}{11}x & = &15\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{15}{11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+14}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-9x } & = & -14 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -14 \color{blue}{-14} \\\Leftrightarrow &-17x & = &-28\\\Leftrightarrow & \color{red}{-17}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-28}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{28}{17} } & & \\ & V = \left\{ \frac{28}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-5}& = & -11 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5-9x } & = & -11 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & 13x \color{blue}{-9x } & = & -11 \color{blue}{+5} \\\Leftrightarrow &4x & = &-6\\\Leftrightarrow & \color{red}{4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-6}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+1}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1-13x } & = & 1 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & 1 \color{blue}{-1} \\\Leftrightarrow &2x & = &0\\\Leftrightarrow & \color{red}{2}x & = &0\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{0}{2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+13}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13+11x } & = & 1 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 1 \color{blue}{-13} \\\Leftrightarrow &15x & = &-12\\\Leftrightarrow & \color{red}{15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-12}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+6}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-x } & = & 4 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 4 \color{blue}{-6} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+3}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-x } & = & -14 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -14 \color{blue}{-3} \\\Leftrightarrow &-7x & = &-17\\\Leftrightarrow & \color{red}{-7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-14}& = & 10 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14-10x } & = & 10 \color{red}{ +10x }\color{blue}{+14-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & 10 \color{blue}{+14} \\\Leftrightarrow &-x & = &24\\\Leftrightarrow & \color{red}{-}x & = &24\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{24}{-1} \\\Leftrightarrow & \color{green}{ x = -24 } & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)