Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-14}& = & 3 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14-10x } & = & 3 \color{red}{ +10x }\color{blue}{+14-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & 3 \color{blue}{+14} \\\Leftrightarrow &3x & = &17\\\Leftrightarrow & \color{red}{3}x & = &17\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{17}{3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-9}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-9}\color{blue}{+9-13x } & = & 4 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &-28x & = &13\\\Leftrightarrow & \color{red}{-28}x & = &13\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{13}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{28} } & & \\ & V = \left\{ \frac{-13}{28} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-8}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-x } & = & 5 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{+8} \\\Leftrightarrow &-6x & = &13\\\Leftrightarrow & \color{red}{-6}x & = &13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+15}& = & -11 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-9x } & = & -11 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &-7x & = &-26\\\Leftrightarrow & \color{red}{-7}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-26}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{26}{7} } & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{-1}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1-9x } & = & -10 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -10 \color{blue}{+1} \\\Leftrightarrow &-13x & = &-9\\\Leftrightarrow & \color{red}{-13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-8}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-x } & = & -15 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &-6x & = &-7\\\Leftrightarrow & \color{red}{-6}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-12}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12-x } & = & -2 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &6x & = &10\\\Leftrightarrow & \color{red}{6}x & = &10\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{10}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+7}\color{blue}{-7-x } & = & -7 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &-4x & = &-14\\\Leftrightarrow & \color{red}{-4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-14}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+9}& = & 5 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9-5x } & = & 5 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & 5 \color{blue}{-9} \\\Leftrightarrow &8x & = &-4\\\Leftrightarrow & \color{red}{8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+12}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+12}\color{blue}{-12+7x } & = & -3 \color{red}{ -7x }\color{blue}{-12+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -3 \color{blue}{-12} \\\Leftrightarrow &22x & = &-15\\\Leftrightarrow & \color{red}{22}x & = &-15\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-15}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{22} } & & \\ & V = \left\{ \frac{-15}{22} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+13}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-11x } & = & 12 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 12 \color{blue}{-13} \\\Leftrightarrow &-21x & = &-1\\\Leftrightarrow & \color{red}{-21}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-1}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{1}{21} } & & \\ & V = \left\{ \frac{1}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12-x } & = & 7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 7 \color{blue}{+12} \\\Leftrightarrow &-8x & = &19\\\Leftrightarrow & \color{red}{-8}x & = &19\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{19}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{8} } & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)