Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-15}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15-13x } & = & 7 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & 7 \color{blue}{+15} \\\Leftrightarrow &-9x & = &22\\\Leftrightarrow & \color{red}{-9}x & = &22\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{22}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{9} } & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+5}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5-7x } & = & -11 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &3x & = &-16\\\Leftrightarrow & \color{red}{3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-3}& = & 5 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-14x } & = & 5 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 5 \color{blue}{+3} \\\Leftrightarrow &-27x & = &8\\\Leftrightarrow & \color{red}{-27}x & = &8\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{8}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{27} } & & \\ & V = \left\{ \frac{-8}{27} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8-x } & = & -3 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &8x & = &-11\\\Leftrightarrow & \color{red}{8}x & = &-11\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-11}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-x } & = & -8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &-13x & = &-12\\\Leftrightarrow & \color{red}{-13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+4}& = & -3 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+4}\color{blue}{-4-10x } & = & -3 \color{red}{ +10x }\color{blue}{-4-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-1}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1-7x } & = & 2 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &-10x & = &3\\\Leftrightarrow & \color{red}{-10}x & = &3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-x } & = & -11 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -11 \color{blue}{-2} \\\Leftrightarrow &-11x & = &-13\\\Leftrightarrow & \color{red}{-11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-3}& = & -6 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3+14x } & = & -6 \color{red}{ -14x }\color{blue}{+3+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -6 \color{blue}{+3} \\\Leftrightarrow &19x & = &-3\\\Leftrightarrow & \color{red}{19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+2}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2-x } & = & -13 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -13 \color{blue}{-2} \\\Leftrightarrow &-5x & = &-15\\\Leftrightarrow & \color{red}{-5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-15}{-5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+11}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-x } & = & 7 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{-11} \\\Leftrightarrow &-9x & = &-4\\\Leftrightarrow & \color{red}{-9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+9}& = & 1 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+9}\color{blue}{-9+9x } & = & 1 \color{red}{ -9x }\color{blue}{-9+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 1 \color{blue}{-9} \\\Leftrightarrow &14x & = &-8\\\Leftrightarrow & \color{red}{14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-8}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)