Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-15}& = & -13 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15-14x } & = & -13 \color{red}{ +14x }\color{blue}{+15-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & -13 \color{blue}{+15} \\\Leftrightarrow &-x & = &2\\\Leftrightarrow & \color{red}{-}x & = &2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{2}{-1} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-8}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-8}\color{blue}{+8-x } & = & -4 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &-7x & = &4\\\Leftrightarrow & \color{red}{-7}x & = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+14}& = & -2 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14-6x } & = & -2 \color{red}{ +6x }\color{blue}{-14-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & -2 \color{blue}{-14} \\\Leftrightarrow &-x & = &-16\\\Leftrightarrow & \color{red}{-}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-16}{-1} \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+7}& = & -1 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7+9x } & = & -1 \color{red}{ -9x }\color{blue}{-7+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -1 \color{blue}{-7} \\\Leftrightarrow &14x & = &-8\\\Leftrightarrow & \color{red}{14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-8}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-x } & = & -14 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -14 \color{blue}{+15} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+8}& = & 13 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8+13x } & = & 13 \color{red}{ -13x }\color{blue}{-8+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 13 \color{blue}{-8} \\\Leftrightarrow &22x & = &5\\\Leftrightarrow & \color{red}{22}x & = &5\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{5}{22} \\\Leftrightarrow & \color{green}{ x = \frac{5}{22} } & & \\ & V = \left\{ \frac{5}{22} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-12}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12-x } & = & 2 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &8x & = &14\\\Leftrightarrow & \color{red}{8}x & = &14\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{14}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-2}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2-x } & = & 2 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 2 \color{blue}{+2} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-1}& = & 15 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1+15x } & = & 15 \color{red}{ -15x }\color{blue}{+1+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &14x & = &16\\\Leftrightarrow & \color{red}{14}x & = &16\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{16}{14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+2}& = & 9 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2+15x } & = & 9 \color{red}{ -15x }\color{blue}{-2+15x } \\\Leftrightarrow & 13x \color{blue}{+15x } & = & 9 \color{blue}{-2} \\\Leftrightarrow &28x & = &7\\\Leftrightarrow & \color{red}{28}x & = &7\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}} & = & \frac{7}{28} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & -3 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-6}& = & 1 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-14x } & = & 1 \color{red}{ +14x }\color{blue}{+6-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &-25x & = &7\\\Leftrightarrow & \color{red}{-25}x & = &7\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{7}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{25} } & & \\ & V = \left\{ \frac{-7}{25} \right\} & \\\end{align}\)