Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-14}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14-13x } & = & 15 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 15 \color{blue}{+14} \\\Leftrightarrow &-5x & = &29\\\Leftrightarrow & \color{red}{-5}x & = &29\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{29}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{5} } & & \\ & V = \left\{ \frac{-29}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-3}& = & -10 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3-5x } & = & -10 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-4}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-x } & = & 11 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &-5x & = &15\\\Leftrightarrow & \color{red}{-5}x & = &15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{15}{-5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+3}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3-x } & = & 6 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 6 \color{blue}{-3} \\\Leftrightarrow &7x & = &3\\\Leftrightarrow & \color{red}{7}x & = &3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+9}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9-x } & = & 15 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 15 \color{blue}{-9} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+8}& = & 4 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8-14x } & = & 4 \color{red}{ +14x }\color{blue}{-8-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & 4 \color{blue}{-8} \\\Leftrightarrow &-x & = &-4\\\Leftrightarrow & \color{red}{-}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-4}{-1} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-4}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-x } & = & 15 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 15 \color{blue}{+4} \\\Leftrightarrow &-12x & = &19\\\Leftrightarrow & \color{red}{-12}x & = &19\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{19}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{12} } & & \\ & V = \left\{ \frac{-19}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-8}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-8}\color{blue}{+8-x } & = & -13 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &-7x & = &-5\\\Leftrightarrow & \color{red}{-7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-4}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4-x } & = & -11 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -11 \color{blue}{+4} \\\Leftrightarrow &3x & = &-7\\\Leftrightarrow & \color{red}{3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{-11}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11-9x } & = & 12 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & x \color{blue}{-9x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &-8x & = &23\\\Leftrightarrow & \color{red}{-8}x & = &23\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{23}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{8} } & & \\ & V = \left\{ \frac{-23}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+3}& = & -5 \color{red}{ -14x } \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3+14x } & = & -5 \color{red}{ -14x }\color{blue}{-3+14x } \\\Leftrightarrow & -x \color{blue}{+14x } & = & -5 \color{blue}{-3} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+8}& = & -10 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8-10x } & = & -10 \color{red}{ +10x }\color{blue}{-8-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & -10 \color{blue}{-8} \\\Leftrightarrow &-3x & = &-18\\\Leftrightarrow & \color{red}{-3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-18}{-3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)