Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (3x-7)& = & 4 \color{red}{+} (12+x) \\\Leftrightarrow & 6x-14& = &4+12+x \\\Leftrightarrow & 6x \color{red}{-14} & = &16 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 6x-x& = &16+14 \\\Leftrightarrow & 5x& = &30 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{30}{ \color{red}{5} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-3x+2)& = & 6 \color{red}{-} (-11+x) \\\Leftrightarrow & -6x+4& = &6+11-x \\\Leftrightarrow & -6x \color{red}{+4} & = &17 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -6x+x& = &17-4 \\\Leftrightarrow & -5x& = &13 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{13}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-13}{5} & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-3x+4)& = & -15 \color{red}{+} (13+x) \\\Leftrightarrow & -6x+8& = &-15+13+x \\\Leftrightarrow & -6x \color{red}{+8} & = &-2 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -6x-x& = &-2-8 \\\Leftrightarrow & -7x& = &-10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-4x-2)& = & 12 \color{red}{+} (-9+x) \\\Leftrightarrow & -8x-4& = &12-9+x \\\Leftrightarrow & -8x \color{red}{-4} & = &3 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -8x-x& = &3+4 \\\Leftrightarrow & -9x& = &7 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{7}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-7}{9} & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (4x-3)& = & -10 \color{red}{-} (7+x) \\\Leftrightarrow & 20x-15& = &-10-7-x \\\Leftrightarrow & 20x \color{red}{-15} & = &-17 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 20x+x& = &-17+15 \\\Leftrightarrow & 21x& = &-2 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-2}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (3x-4)& = & -6 \color{red}{+} (10+x) \\\Leftrightarrow & 12x-16& = &-6+10+x \\\Leftrightarrow & 12x \color{red}{-16} & = &4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 12x-x& = &4+16 \\\Leftrightarrow & 11x& = &20 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{20}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{20}{11} & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-3x-3)& = & 10 \color{red}{-} (-6-4x) \\\Leftrightarrow & -9x-9& = &10+6+4x \\\Leftrightarrow & -9x \color{red}{-9} & = &16 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{-9} \color{blue}{+9} \color{blue}{-4x} & = &16 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+9} \\\Leftrightarrow & -9x-4x& = &16+9 \\\Leftrightarrow & -13x& = &25 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{25}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-25}{13} & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-4x+5)& = & 13 \color{red}{+} (-4+x) \\\Leftrightarrow & -20x+25& = &13-4+x \\\Leftrightarrow & -20x \color{red}{+25} & = &9 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -20x-x& = &9-25 \\\Leftrightarrow & -21x& = &-16 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-16}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{16}{21} & & \\ & V = \left\{ \frac{16}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (3x+6)& = & -12 \color{red}{+} (9+x) \\\Leftrightarrow & 12x+24& = &-12+9+x \\\Leftrightarrow & 12x \color{red}{+24} & = &-3 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 12x-x& = &-3-24 \\\Leftrightarrow & 11x& = &-27 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-27}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-27}{11} & & \\ & V = \left\{ \frac{-27}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-6x+5)& = & 2 \color{red}{+} (-9+x) \\\Leftrightarrow & -30x+25& = &2-9+x \\\Leftrightarrow & -30x \color{red}{+25} & = &-7 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -30x-x& = &-7-25 \\\Leftrightarrow & -31x& = &-32 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-32}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{32}{31} & & \\ & V = \left\{ \frac{32}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (6x+1)& = & 11 \color{red}{+} (5+x) \\\Leftrightarrow & 24x+4& = &11+5+x \\\Leftrightarrow & 24x \color{red}{+4} & = &16 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 24x-x& = &16-4 \\\Leftrightarrow & 23x& = &12 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{12}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{12}{23} & & \\ & V = \left\{ \frac{12}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (4x+1)& = & 8 \color{red}{-} (-9+x) \\\Leftrightarrow & 12x+3& = &8+9-x \\\Leftrightarrow & 12x \color{red}{+3} & = &17 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 12x+x& = &17-3 \\\Leftrightarrow & 13x& = &14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)