Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+4}& = &9 \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4} & = &9\color{blue}{-4} \\\Leftrightarrow &3x & = &5\\\Leftrightarrow & \color{red}{3}x & = &5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-6}& = &-3 \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6} & = &-3\color{blue}{+6} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-3}& = &9 \\\Leftrightarrow & 4x \color{red}{-3}\color{blue}{+3} & = &9\color{blue}{+3} \\\Leftrightarrow &4x & = &12\\\Leftrightarrow & \color{red}{4}x & = &12\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{12}{4} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-2}& = &-7 \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2} & = &-7\color{blue}{+2} \\\Leftrightarrow &4x & = &-5\\\Leftrightarrow & \color{red}{4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-5}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+9}& = &-14 \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9} & = &-14\color{blue}{-9} \\\Leftrightarrow &-13x & = &-23\\\Leftrightarrow & \color{red}{-13}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-23}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{23}{13} } & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+5}& = &-6 \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5} & = &-6\color{blue}{-5} \\\Leftrightarrow &14x & = &-11\\\Leftrightarrow & \color{red}{14}x & = &-11\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-11}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+2}& = &-3 \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2} & = &-3\color{blue}{-2} \\\Leftrightarrow &-3x & = &-5\\\Leftrightarrow & \color{red}{-3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+14}& = &-3 \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14} & = &-3\color{blue}{-14} \\\Leftrightarrow &4x & = &-17\\\Leftrightarrow & \color{red}{4}x & = &-17\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-17}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{4} } & & \\ & V = \left\{ \frac{-17}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+11}& = &-5 \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11} & = &-5\color{blue}{-11} \\\Leftrightarrow &8x & = &-16\\\Leftrightarrow & \color{red}{8}x & = &-16\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-16}{8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+11}& = &6 \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11} & = &6\color{blue}{-11} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-4}& = &9 \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4} & = &9\color{blue}{+4} \\\Leftrightarrow &-10x & = &13\\\Leftrightarrow & \color{red}{-10}x & = &13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+1}& = &-4 \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1} & = &-4\color{blue}{-1} \\\Leftrightarrow &4x & = &-5\\\Leftrightarrow & \color{red}{4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-5}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)