Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-x } & = & 5 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &-16x & = &4\\\Leftrightarrow & \color{red}{-16}x & = &4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-15}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15-x } & = & 2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 2 \color{blue}{+15} \\\Leftrightarrow &-13x & = &17\\\Leftrightarrow & \color{red}{-13}x & = &17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-14}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-x } & = & 6 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &-10x & = &20\\\Leftrightarrow & \color{red}{-10}x & = &20\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{20}{-10} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+7}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7-x } & = & -4 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -4 \color{blue}{-7} \\\Leftrightarrow &-8x & = &-11\\\Leftrightarrow & \color{red}{-8}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+6}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6+11x } & = & -10 \color{red}{ -11x }\color{blue}{-6+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -10 \color{blue}{-6} \\\Leftrightarrow &17x & = &-16\\\Leftrightarrow & \color{red}{17}x & = &-16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+9}& = & -9 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9+14x } & = & -9 \color{red}{ -14x }\color{blue}{-9+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &29x & = &-18\\\Leftrightarrow & \color{red}{29}x & = &-18\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-18}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{29} } & & \\ & V = \left\{ \frac{-18}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+4}& = & 12 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-4x } & = & 12 \color{red}{ +4x }\color{blue}{-4-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &-19x & = &8\\\Leftrightarrow & \color{red}{-19}x & = &8\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{8}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{19} } & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+4}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & -1 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -1 \color{blue}{-4} \\\Leftrightarrow &-14x & = &-5\\\Leftrightarrow & \color{red}{-14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-10}& = & 3 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-10}\color{blue}{+10-10x } & = & 3 \color{red}{ +10x }\color{blue}{+10-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 3 \color{blue}{+10} \\\Leftrightarrow &-13x & = &13\\\Leftrightarrow & \color{red}{-13}x & = &13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{13}{-13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+8}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-x } & = & 3 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 3 \color{blue}{-8} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+14}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14-13x } & = & -13 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -13 \color{blue}{-14} \\\Leftrightarrow &-28x & = &-27\\\Leftrightarrow & \color{red}{-28}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-27}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{27}{28} } & & \\ & V = \left\{ \frac{27}{28} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{-3}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3+13x } & = & -5 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &27x & = &-2\\\Leftrightarrow & \color{red}{27}x & = &-2\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-2}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{27} } & & \\ & V = \left\{ \frac{-2}{27} \right\} & \\\end{align}\)