Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+3}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3-13x } & = & -10 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & -10 \color{blue}{-3} \\\Leftrightarrow &-12x & = &-13\\\Leftrightarrow & \color{red}{-12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-4}& = & 7 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4-4x } & = & 7 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 7 \color{blue}{+4} \\\Leftrightarrow &11x & = &11\\\Leftrightarrow & \color{red}{11}x & = &11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{11}{11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+15}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15+13x } & = & -3 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -3 \color{blue}{-15} \\\Leftrightarrow &23x & = &-18\\\Leftrightarrow & \color{red}{23}x & = &-18\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-18}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{23} } & & \\ & V = \left\{ \frac{-18}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+7}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7-x } & = & 3 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &4x & = &-4\\\Leftrightarrow & \color{red}{4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-4}{4} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-3}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3+13x } & = & 1 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 1 \color{blue}{+3} \\\Leftrightarrow &22x & = &4\\\Leftrightarrow & \color{red}{22}x & = &4\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{4}{22} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-7}& = & -2 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7+15x } & = & -2 \color{red}{ -15x }\color{blue}{+7+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -2 \color{blue}{+7} \\\Leftrightarrow &23x & = &5\\\Leftrightarrow & \color{red}{23}x & = &5\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{5}{23} \\\Leftrightarrow & \color{green}{ x = \frac{5}{23} } & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+1}\color{blue}{-1-x } & = & -10 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -10 \color{blue}{-1} \\\Leftrightarrow &2x & = &-11\\\Leftrightarrow & \color{red}{2}x & = &-11\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-11}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-x } & = & -12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &-11x & = &-15\\\Leftrightarrow & \color{red}{-11}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-9}& = & -3 \color{red}{ +6x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9-6x } & = & -3 \color{red}{ +6x }\color{blue}{+9-6x } \\\Leftrightarrow & -x \color{blue}{-6x } & = & -3 \color{blue}{+9} \\\Leftrightarrow &-7x & = &6\\\Leftrightarrow & \color{red}{-7}x & = &6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-5}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-5x } & = & -2 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -2 \color{blue}{+5} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+1}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-5x } & = & 10 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 10 \color{blue}{-1} \\\Leftrightarrow &-9x & = &9\\\Leftrightarrow & \color{red}{-9}x & = &9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{9}{-9} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+13}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-13x } & = & 14 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 14 \color{blue}{-13} \\\Leftrightarrow &-19x & = &1\\\Leftrightarrow & \color{red}{-19}x & = &1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)