Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{11})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -6x+\frac{6}{11}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{+54} & = & \color{red}{-693x} +22 \\\Leftrightarrow & -594x \color{red}{+54} \color{blue}{-54} \color{blue}{+693x} & = & \color{red}{-693x} +22 \color{blue}{+693x} \color{blue}{-54} \\\Leftrightarrow & -594x+693x& = & 22-54 \\\Leftrightarrow & \color{red}{99} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{99} & & \\ & V = \left\{ \frac{-32}{99} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{4})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -6x-\frac{15}{4}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-264}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -264x \color{red}{-165} & = & \color{red}{308x} +24 \\\Leftrightarrow & -264x \color{red}{-165} \color{blue}{+165} \color{blue}{-308x} & = & \color{red}{308x} +24 \color{blue}{-308x} \color{blue}{+165} \\\Leftrightarrow & -264x-308x& = & 24+165 \\\Leftrightarrow & \color{red}{-572} x& = & 189 \\\Leftrightarrow & x = \frac{189}{-572} & & \\\Leftrightarrow & x = \frac{-189}{572} & & \\ & V = \left\{ \frac{-189}{572} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{3}{10})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x-\frac{9}{10}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-360}{ \color{blue}{30} }x- \frac{27}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{80}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -360x \color{red}{-27} & = & \color{red}{150x} +80 \\\Leftrightarrow & -360x \color{red}{-27} \color{blue}{+27} \color{blue}{-150x} & = & \color{red}{150x} +80 \color{blue}{-150x} \color{blue}{+27} \\\Leftrightarrow & -360x-150x& = & 80+27 \\\Leftrightarrow & \color{red}{-510} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-510} & & \\\Leftrightarrow & x = \frac{-107}{510} & & \\ & V = \left\{ \frac{-107}{510} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{9})& = & -3x+\frac{3}{4} \\\Leftrightarrow & 28x-\frac{14}{9}& = & -3x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{1008}{ \color{blue}{36} }x- \frac{56}{ \color{blue}{36} })& = & (\frac{-108}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 1008x \color{red}{-56} & = & \color{red}{-108x} +27 \\\Leftrightarrow & 1008x \color{red}{-56} \color{blue}{+56} \color{blue}{+108x} & = & \color{red}{-108x} +27 \color{blue}{+108x} \color{blue}{+56} \\\Leftrightarrow & 1008x+108x& = & 27+56 \\\Leftrightarrow & \color{red}{1116} x& = & 83 \\\Leftrightarrow & x = \frac{83}{1116} & & \\ & V = \left\{ \frac{83}{1116} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{5})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -24x-\frac{18}{5}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x- \frac{126}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{-126} & = & \color{red}{-245x} +40 \\\Leftrightarrow & -840x \color{red}{-126} \color{blue}{+126} \color{blue}{+245x} & = & \color{red}{-245x} +40 \color{blue}{+245x} \color{blue}{+126} \\\Leftrightarrow & -840x+245x& = & 40+126 \\\Leftrightarrow & \color{red}{-595} x& = & 166 \\\Leftrightarrow & x = \frac{166}{-595} & & \\\Leftrightarrow & x = \frac{-166}{595} & & \\ & V = \left\{ \frac{-166}{595} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & -5x+\frac{9}{5} \\\Leftrightarrow & -12x-\frac{18}{11}& = & -5x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-90} & = & \color{red}{-275x} +99 \\\Leftrightarrow & -660x \color{red}{-90} \color{blue}{+90} \color{blue}{+275x} & = & \color{red}{-275x} +99 \color{blue}{+275x} \color{blue}{+90} \\\Leftrightarrow & -660x+275x& = & 99+90 \\\Leftrightarrow & \color{red}{-385} x& = & 189 \\\Leftrightarrow & x = \frac{189}{-385} & & \\\Leftrightarrow & x = \frac{-27}{55} & & \\ & V = \left\{ \frac{-27}{55} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{11})& = & -8x+\frac{10}{7} \\\Leftrightarrow & -15x+\frac{6}{11}& = & -8x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{-616}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+42} & = & \color{red}{-616x} +110 \\\Leftrightarrow & -1155x \color{red}{+42} \color{blue}{-42} \color{blue}{+616x} & = & \color{red}{-616x} +110 \color{blue}{+616x} \color{blue}{-42} \\\Leftrightarrow & -1155x+616x& = & 110-42 \\\Leftrightarrow & \color{red}{-539} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-539} & & \\\Leftrightarrow & x = \frac{-68}{539} & & \\ & V = \left\{ \frac{-68}{539} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{7})& = & 3x+\frac{2}{11} \\\Leftrightarrow & 25x-\frac{15}{7}& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x- \frac{165}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{-165} & = & \color{red}{231x} +14 \\\Leftrightarrow & 1925x \color{red}{-165} \color{blue}{+165} \color{blue}{-231x} & = & \color{red}{231x} +14 \color{blue}{-231x} \color{blue}{+165} \\\Leftrightarrow & 1925x-231x& = & 14+165 \\\Leftrightarrow & \color{red}{1694} x& = & 179 \\\Leftrightarrow & x = \frac{179}{1694} & & \\ & V = \left\{ \frac{179}{1694} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{7})& = & -3x+\frac{9}{5} \\\Leftrightarrow & 10x-\frac{10}{7}& = & -3x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-50} & = & \color{red}{-105x} +63 \\\Leftrightarrow & 350x \color{red}{-50} \color{blue}{+50} \color{blue}{+105x} & = & \color{red}{-105x} +63 \color{blue}{+105x} \color{blue}{+50} \\\Leftrightarrow & 350x+105x& = & 63+50 \\\Leftrightarrow & \color{red}{455} x& = & 113 \\\Leftrightarrow & x = \frac{113}{455} & & \\ & V = \left\{ \frac{113}{455} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{5}{11})& = & 3x+\frac{5}{2} \\\Leftrightarrow & 8x+\frac{10}{11}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{176}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 176x \color{red}{+20} & = & \color{red}{66x} +55 \\\Leftrightarrow & 176x \color{red}{+20} \color{blue}{-20} \color{blue}{-66x} & = & \color{red}{66x} +55 \color{blue}{-66x} \color{blue}{-20} \\\Leftrightarrow & 176x-66x& = & 55-20 \\\Leftrightarrow & \color{red}{110} x& = & 35 \\\Leftrightarrow & x = \frac{35}{110} & & \\\Leftrightarrow & x = \frac{7}{22} & & \\ & V = \left\{ \frac{7}{22} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{11})& = & -8x+\frac{10}{3} \\\Leftrightarrow & 21x-\frac{21}{11}& = & -8x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x- \frac{63}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{-63} & = & \color{red}{-264x} +110 \\\Leftrightarrow & 693x \color{red}{-63} \color{blue}{+63} \color{blue}{+264x} & = & \color{red}{-264x} +110 \color{blue}{+264x} \color{blue}{+63} \\\Leftrightarrow & 693x+264x& = & 110+63 \\\Leftrightarrow & \color{red}{957} x& = & 173 \\\Leftrightarrow & x = \frac{173}{957} & & \\ & V = \left\{ \frac{173}{957} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{4})& = & 5x+\frac{7}{10} \\\Leftrightarrow & -12x-\frac{15}{4}& = & 5x+\frac{7}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{14}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{-75} & = & \color{red}{100x} +14 \\\Leftrightarrow & -240x \color{red}{-75} \color{blue}{+75} \color{blue}{-100x} & = & \color{red}{100x} +14 \color{blue}{-100x} \color{blue}{+75} \\\Leftrightarrow & -240x-100x& = & 14+75 \\\Leftrightarrow & \color{red}{-340} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-340} & & \\\Leftrightarrow & x = \frac{-89}{340} & & \\ & V = \left\{ \frac{-89}{340} \right\} & \\\end{align}\)