Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{2}{11})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 15x-\frac{10}{11}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{-30} & = & \color{red}{-231x} +110 \\\Leftrightarrow & 495x \color{red}{-30} \color{blue}{+30} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{+30} \\\Leftrightarrow & 495x+231x& = & 110+30 \\\Leftrightarrow & \color{red}{726} x& = & 140 \\\Leftrightarrow & x = \frac{140}{726} & & \\\Leftrightarrow & x = \frac{70}{363} & & \\ & V = \left\{ \frac{70}{363} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{5}{6})& = & -8x+\frac{4}{11} \\\Leftrightarrow & 21x+\frac{35}{6}& = & -8x+\frac{4}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{1386}{ \color{blue}{66} }x+ \frac{385}{ \color{blue}{66} })& = & (\frac{-528}{ \color{blue}{66} }x+ \frac{24}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 1386x \color{red}{+385} & = & \color{red}{-528x} +24 \\\Leftrightarrow & 1386x \color{red}{+385} \color{blue}{-385} \color{blue}{+528x} & = & \color{red}{-528x} +24 \color{blue}{+528x} \color{blue}{-385} \\\Leftrightarrow & 1386x+528x& = & 24-385 \\\Leftrightarrow & \color{red}{1914} x& = & -361 \\\Leftrightarrow & x = \frac{-361}{1914} & & \\ & V = \left\{ \frac{-361}{1914} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{5}{3})& = & 7x+\frac{2}{5} \\\Leftrightarrow & -10x+\frac{10}{3}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{+50} & = & \color{red}{105x} +6 \\\Leftrightarrow & -150x \color{red}{+50} \color{blue}{-50} \color{blue}{-105x} & = & \color{red}{105x} +6 \color{blue}{-105x} \color{blue}{-50} \\\Leftrightarrow & -150x-105x& = & 6-50 \\\Leftrightarrow & \color{red}{-255} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{-255} & & \\\Leftrightarrow & x = \frac{44}{255} & & \\ & V = \left\{ \frac{44}{255} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{3}{11})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 12x-\frac{9}{11}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{264}{ \color{blue}{22} }x- \frac{18}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 264x \color{red}{-18} & = & \color{red}{-110x} +99 \\\Leftrightarrow & 264x \color{red}{-18} \color{blue}{+18} \color{blue}{+110x} & = & \color{red}{-110x} +99 \color{blue}{+110x} \color{blue}{+18} \\\Leftrightarrow & 264x+110x& = & 99+18 \\\Leftrightarrow & \color{red}{374} x& = & 117 \\\Leftrightarrow & x = \frac{117}{374} & & \\ & V = \left\{ \frac{117}{374} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{11})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -10x+\frac{10}{11}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1100}{ \color{blue}{110} }x+ \frac{100}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1100x \color{red}{+100} & = & \color{red}{-770x} +99 \\\Leftrightarrow & -1100x \color{red}{+100} \color{blue}{-100} \color{blue}{+770x} & = & \color{red}{-770x} +99 \color{blue}{+770x} \color{blue}{-100} \\\Leftrightarrow & -1100x+770x& = & 99-100 \\\Leftrightarrow & \color{red}{-330} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-330} & & \\\Leftrightarrow & x = \frac{1}{330} & & \\ & V = \left\{ \frac{1}{330} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{2}{5})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -10x-\frac{4}{5}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{-44} & = & \color{red}{-385x} +10 \\\Leftrightarrow & -550x \color{red}{-44} \color{blue}{+44} \color{blue}{+385x} & = & \color{red}{-385x} +10 \color{blue}{+385x} \color{blue}{+44} \\\Leftrightarrow & -550x+385x& = & 10+44 \\\Leftrightarrow & \color{red}{-165} x& = & 54 \\\Leftrightarrow & x = \frac{54}{-165} & & \\\Leftrightarrow & x = \frac{-18}{55} & & \\ & V = \left\{ \frac{-18}{55} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{7})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -16x-\frac{20}{7}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1120}{ \color{blue}{70} }x- \frac{200}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1120x \color{red}{-200} & = & \color{red}{490x} +21 \\\Leftrightarrow & -1120x \color{red}{-200} \color{blue}{+200} \color{blue}{-490x} & = & \color{red}{490x} +21 \color{blue}{-490x} \color{blue}{+200} \\\Leftrightarrow & -1120x-490x& = & 21+200 \\\Leftrightarrow & \color{red}{-1610} x& = & 221 \\\Leftrightarrow & x = \frac{221}{-1610} & & \\\Leftrightarrow & x = \frac{-221}{1610} & & \\ & V = \left\{ \frac{-221}{1610} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{4}{3})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -10x+\frac{20}{3}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-30}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -30x \color{red}{+20} & = & \color{red}{21x} +2 \\\Leftrightarrow & -30x \color{red}{+20} \color{blue}{-20} \color{blue}{-21x} & = & \color{red}{21x} +2 \color{blue}{-21x} \color{blue}{-20} \\\Leftrightarrow & -30x-21x& = & 2-20 \\\Leftrightarrow & \color{red}{-51} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-51} & & \\\Leftrightarrow & x = \frac{6}{17} & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{3})& = & 9x+\frac{7}{10} \\\Leftrightarrow & 8x+\frac{8}{3}& = & 9x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{240}{ \color{blue}{30} }x+ \frac{80}{ \color{blue}{30} })& = & (\frac{270}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 240x \color{red}{+80} & = & \color{red}{270x} +21 \\\Leftrightarrow & 240x \color{red}{+80} \color{blue}{-80} \color{blue}{-270x} & = & \color{red}{270x} +21 \color{blue}{-270x} \color{blue}{-80} \\\Leftrightarrow & 240x-270x& = & 21-80 \\\Leftrightarrow & \color{red}{-30} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-30} & & \\\Leftrightarrow & x = \frac{59}{30} & & \\ & V = \left\{ \frac{59}{30} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{11})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -10x-\frac{6}{11}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-440}{ \color{blue}{44} }x- \frac{24}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -440x \color{red}{-24} & = & \color{red}{-308x} +33 \\\Leftrightarrow & -440x \color{red}{-24} \color{blue}{+24} \color{blue}{+308x} & = & \color{red}{-308x} +33 \color{blue}{+308x} \color{blue}{+24} \\\Leftrightarrow & -440x+308x& = & 33+24 \\\Leftrightarrow & \color{red}{-132} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-132} & & \\\Leftrightarrow & x = \frac{-19}{44} & & \\ & V = \left\{ \frac{-19}{44} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{3})& = & -3x+\frac{7}{12} \\\Leftrightarrow & -35x-\frac{35}{3}& = & -3x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-420}{ \color{blue}{12} }x- \frac{140}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -420x \color{red}{-140} & = & \color{red}{-36x} +7 \\\Leftrightarrow & -420x \color{red}{-140} \color{blue}{+140} \color{blue}{+36x} & = & \color{red}{-36x} +7 \color{blue}{+36x} \color{blue}{+140} \\\Leftrightarrow & -420x+36x& = & 7+140 \\\Leftrightarrow & \color{red}{-384} x& = & 147 \\\Leftrightarrow & x = \frac{147}{-384} & & \\\Leftrightarrow & x = \frac{-49}{128} & & \\ & V = \left\{ \frac{-49}{128} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{9})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -12x-\frac{20}{9}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-108}{ \color{blue}{9} }x- \frac{20}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -108x \color{red}{-20} & = & \color{red}{-45x} +6 \\\Leftrightarrow & -108x \color{red}{-20} \color{blue}{+20} \color{blue}{+45x} & = & \color{red}{-45x} +6 \color{blue}{+45x} \color{blue}{+20} \\\Leftrightarrow & -108x+45x& = & 6+20 \\\Leftrightarrow & \color{red}{-63} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-63} & & \\\Leftrightarrow & x = \frac{-26}{63} & & \\ & V = \left\{ \frac{-26}{63} \right\} & \\\end{align}\)