Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-5x+2)& = & 5 \color{red}{+} (6+x) \\\Leftrightarrow & -20x+8& = &5+6+x \\\Leftrightarrow & -20x \color{red}{+8} & = &11 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -20x-x& = &11-8 \\\Leftrightarrow & -21x& = &3 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{3}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x+1)& = & -11 \color{red}{+} (7+4x) \\\Leftrightarrow & 5x+5& = &-11+7+4x \\\Leftrightarrow & 5x \color{red}{+5} & = &-4 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{+5} \color{blue}{-5} \color{blue}{-4x} & = &-4 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-5} \\\Leftrightarrow & 5x-4x& = &-4-5 \\\Leftrightarrow & x& = &-9 \\ & V = \left\{ -9 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (4x-7)& = & -4 \color{red}{-} (12+x) \\\Leftrightarrow & 20x-35& = &-4-12-x \\\Leftrightarrow & 20x \color{red}{-35} & = &-16 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & 20x+x& = &-16+35 \\\Leftrightarrow & 21x& = &19 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{19}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{19}{21} & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (3x-1)& = & 5 \color{red}{+} (6-2x) \\\Leftrightarrow & 15x-5& = &5+6-2x \\\Leftrightarrow & 15x \color{red}{-5} & = &11 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-5} \color{blue}{+5} \color{blue}{+2x} & = &11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+5} \\\Leftrightarrow & 15x+2x& = &11+5 \\\Leftrightarrow & 17x& = &16 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{16}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{16}{17} & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-6x-6)& = & -8 \color{red}{-} (-6+x) \\\Leftrightarrow & -24x-24& = &-8+6-x \\\Leftrightarrow & -24x \color{red}{-24} & = &-2 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -24x+x& = &-2+24 \\\Leftrightarrow & -23x& = &22 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{22}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-22}{23} & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x+2)& = & -14 \color{red}{-} (10+x) \\\Leftrightarrow & -24x+8& = &-14-10-x \\\Leftrightarrow & -24x \color{red}{+8} & = &-24 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -24x+x& = &-24-8 \\\Leftrightarrow & -23x& = &-32 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-32}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{32}{23} & & \\ & V = \left\{ \frac{32}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (6x+1)& = & 5 \color{red}{+} (11+x) \\\Leftrightarrow & 30x+5& = &5+11+x \\\Leftrightarrow & 30x \color{red}{+5} & = &16 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & 30x-x& = &16-5 \\\Leftrightarrow & 29x& = &11 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{11}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{11}{29} & & \\ & V = \left\{ \frac{11}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-5x+1)& = & -3 \color{red}{-} (7+x) \\\Leftrightarrow & -10x+2& = &-3-7-x \\\Leftrightarrow & -10x \color{red}{+2} & = &-10 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -10x+x& = &-10-2 \\\Leftrightarrow & -9x& = &-12 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-12}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x+2)& = & -1 \color{red}{+} (-9+x) \\\Leftrightarrow & -2x+4& = &-1-9+x \\\Leftrightarrow & -2x \color{red}{+4} & = &-10 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -2x-x& = &-10-4 \\\Leftrightarrow & -3x& = &-14 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-14}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{14}{3} & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (x+5)& = & 8 \color{red}{+} (4-2x) \\\Leftrightarrow & 5x+25& = &8+4-2x \\\Leftrightarrow & 5x \color{red}{+25} & = &12 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{+25} \color{blue}{-25} \color{blue}{+2x} & = &12 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-25} \\\Leftrightarrow & 5x+2x& = &12-25 \\\Leftrightarrow & 7x& = &-13 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-13}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-13}{7} & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x-6)& = & -10 \color{red}{+} (-11+x) \\\Leftrightarrow & -20x-24& = &-10-11+x \\\Leftrightarrow & -20x \color{red}{-24} & = &-21 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -20x-x& = &-21+24 \\\Leftrightarrow & -21x& = &3 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{3}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x+3)& = & -4 \color{red}{-} (15+x) \\\Leftrightarrow & -16x+12& = &-4-15-x \\\Leftrightarrow & -16x \color{red}{+12} & = &-19 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -16x+x& = &-19-12 \\\Leftrightarrow & -15x& = &-31 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{-31}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{31}{15} & & \\ & V = \left\{ \frac{31}{15} \right\} & \\\end{align}\)