Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-7}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-x } & = & 15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &-16x & = &22\\\Leftrightarrow & \color{red}{-16}x & = &22\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{22}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-10}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-13x } & = & 15 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & 15 \color{blue}{+10} \\\Leftrightarrow &-15x & = &25\\\Leftrightarrow & \color{red}{-15}x & = &25\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{25}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+12}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x } & = & -3 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -3 \color{blue}{-12} \\\Leftrightarrow &-15x & = &-15\\\Leftrightarrow & \color{red}{-15}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-15}{-15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-14}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-7x } & = & 15 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & 15 \color{blue}{+14} \\\Leftrightarrow &-16x & = &29\\\Leftrightarrow & \color{red}{-16}x & = &29\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{29}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{16} } & & \\ & V = \left\{ \frac{-29}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+3}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3-13x } & = & -5 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -5 \color{blue}{-3} \\\Leftrightarrow &-4x & = &-8\\\Leftrightarrow & \color{red}{-4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-8}{-4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-1}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1+7x } & = & -13 \color{red}{ -7x }\color{blue}{+1+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -13 \color{blue}{+1} \\\Leftrightarrow &15x & = &-12\\\Leftrightarrow & \color{red}{15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-12}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-7}& = & 8 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7-12x } & = & 8 \color{red}{ +12x }\color{blue}{+7-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & 8 \color{blue}{+7} \\\Leftrightarrow &-x & = &15\\\Leftrightarrow & \color{red}{-}x & = &15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{15}{-1} \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+10}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10-x } & = & -1 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &2x & = &-11\\\Leftrightarrow & \color{red}{2}x & = &-11\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-11}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-2}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-x } & = & 5 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 5 \color{blue}{+2} \\\Leftrightarrow &-11x & = &7\\\Leftrightarrow & \color{red}{-11}x & = &7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-2}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-x } & = & -13 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -13 \color{blue}{+2} \\\Leftrightarrow &-7x & = &-11\\\Leftrightarrow & \color{red}{-7}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+3}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3-5x } & = & 14 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & x \color{blue}{-5x } & = & 14 \color{blue}{-3} \\\Leftrightarrow &-4x & = &11\\\Leftrightarrow & \color{red}{-4}x & = &11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-6}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x } & = & 11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &-4x & = &17\\\Leftrightarrow & \color{red}{-4}x & = &17\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{17}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{4} } & & \\ & V = \left\{ \frac{-17}{4} \right\} & \\\end{align}\)