Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{2}{11})& = & 2x+\frac{9}{8} \\\Leftrightarrow & 15x-\frac{6}{11}& = & 2x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1320}{ \color{blue}{88} }x- \frac{48}{ \color{blue}{88} })& = & (\frac{176}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1320x \color{red}{-48} & = & \color{red}{176x} +99 \\\Leftrightarrow & 1320x \color{red}{-48} \color{blue}{+48} \color{blue}{-176x} & = & \color{red}{176x} +99 \color{blue}{-176x} \color{blue}{+48} \\\Leftrightarrow & 1320x-176x& = & 99+48 \\\Leftrightarrow & \color{red}{1144} x& = & 147 \\\Leftrightarrow & x = \frac{147}{1144} & & \\ & V = \left\{ \frac{147}{1144} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{7})& = & 9x+\frac{3}{10} \\\Leftrightarrow & -8x-\frac{16}{7}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-560}{ \color{blue}{70} }x- \frac{160}{ \color{blue}{70} })& = & (\frac{630}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -560x \color{red}{-160} & = & \color{red}{630x} +21 \\\Leftrightarrow & -560x \color{red}{-160} \color{blue}{+160} \color{blue}{-630x} & = & \color{red}{630x} +21 \color{blue}{-630x} \color{blue}{+160} \\\Leftrightarrow & -560x-630x& = & 21+160 \\\Leftrightarrow & \color{red}{-1190} x& = & 181 \\\Leftrightarrow & x = \frac{181}{-1190} & & \\\Leftrightarrow & x = \frac{-181}{1190} & & \\ & V = \left\{ \frac{-181}{1190} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{3}{7})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 20x-\frac{15}{7}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x- \frac{15}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{-15} & = & \color{red}{49x} +8 \\\Leftrightarrow & 140x \color{red}{-15} \color{blue}{+15} \color{blue}{-49x} & = & \color{red}{49x} +8 \color{blue}{-49x} \color{blue}{+15} \\\Leftrightarrow & 140x-49x& = & 8+15 \\\Leftrightarrow & \color{red}{91} x& = & 23 \\\Leftrightarrow & x = \frac{23}{91} & & \\ & V = \left\{ \frac{23}{91} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{4}{3})& = & 7x+\frac{8}{5} \\\Leftrightarrow & -10x-\frac{20}{3}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x- \frac{100}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{-100} & = & \color{red}{105x} +24 \\\Leftrightarrow & -150x \color{red}{-100} \color{blue}{+100} \color{blue}{-105x} & = & \color{red}{105x} +24 \color{blue}{-105x} \color{blue}{+100} \\\Leftrightarrow & -150x-105x& = & 24+100 \\\Leftrightarrow & \color{red}{-255} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-255} & & \\\Leftrightarrow & x = \frac{-124}{255} & & \\ & V = \left\{ \frac{-124}{255} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{3}{7})& = & -2x+\frac{8}{11} \\\Leftrightarrow & 15x+\frac{15}{7}& = & -2x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x+ \frac{165}{ \color{blue}{77} })& = & (\frac{-154}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{+165} & = & \color{red}{-154x} +56 \\\Leftrightarrow & 1155x \color{red}{+165} \color{blue}{-165} \color{blue}{+154x} & = & \color{red}{-154x} +56 \color{blue}{+154x} \color{blue}{-165} \\\Leftrightarrow & 1155x+154x& = & 56-165 \\\Leftrightarrow & \color{red}{1309} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{1309} & & \\ & V = \left\{ \frac{-109}{1309} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{7})& = & 7x+\frac{7}{10} \\\Leftrightarrow & -16x-\frac{16}{7}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1120}{ \color{blue}{70} }x- \frac{160}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1120x \color{red}{-160} & = & \color{red}{490x} +49 \\\Leftrightarrow & -1120x \color{red}{-160} \color{blue}{+160} \color{blue}{-490x} & = & \color{red}{490x} +49 \color{blue}{-490x} \color{blue}{+160} \\\Leftrightarrow & -1120x-490x& = & 49+160 \\\Leftrightarrow & \color{red}{-1610} x& = & 209 \\\Leftrightarrow & x = \frac{209}{-1610} & & \\\Leftrightarrow & x = \frac{-209}{1610} & & \\ & V = \left\{ \frac{-209}{1610} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{7})& = & -9x+\frac{9}{7} \\\Leftrightarrow & 10x-\frac{10}{7}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{-10} & = & \color{red}{-63x} +9 \\\Leftrightarrow & 70x \color{red}{-10} \color{blue}{+10} \color{blue}{+63x} & = & \color{red}{-63x} +9 \color{blue}{+63x} \color{blue}{+10} \\\Leftrightarrow & 70x+63x& = & 9+10 \\\Leftrightarrow & \color{red}{133} x& = & 19 \\\Leftrightarrow & x = \frac{19}{133} & & \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{11})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 6x+\frac{6}{11}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{396}{ \color{blue}{66} }x+ \frac{36}{ \color{blue}{66} })& = & (\frac{-330}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 396x \color{red}{+36} & = & \color{red}{-330x} +55 \\\Leftrightarrow & 396x \color{red}{+36} \color{blue}{-36} \color{blue}{+330x} & = & \color{red}{-330x} +55 \color{blue}{+330x} \color{blue}{-36} \\\Leftrightarrow & 396x+330x& = & 55-36 \\\Leftrightarrow & \color{red}{726} x& = & 19 \\\Leftrightarrow & x = \frac{19}{726} & & \\ & V = \left\{ \frac{19}{726} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{2}{9})& = & 4x+\frac{6}{11} \\\Leftrightarrow & -15x-\frac{10}{9}& = & 4x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1485}{ \color{blue}{99} }x- \frac{110}{ \color{blue}{99} })& = & (\frac{396}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1485x \color{red}{-110} & = & \color{red}{396x} +54 \\\Leftrightarrow & -1485x \color{red}{-110} \color{blue}{+110} \color{blue}{-396x} & = & \color{red}{396x} +54 \color{blue}{-396x} \color{blue}{+110} \\\Leftrightarrow & -1485x-396x& = & 54+110 \\\Leftrightarrow & \color{red}{-1881} x& = & 164 \\\Leftrightarrow & x = \frac{164}{-1881} & & \\\Leftrightarrow & x = \frac{-164}{1881} & & \\ & V = \left\{ \frac{-164}{1881} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{11})& = & -5x+\frac{7}{9} \\\Leftrightarrow & -9x-\frac{12}{11}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-891}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -891x \color{red}{-108} & = & \color{red}{-495x} +77 \\\Leftrightarrow & -891x \color{red}{-108} \color{blue}{+108} \color{blue}{+495x} & = & \color{red}{-495x} +77 \color{blue}{+495x} \color{blue}{+108} \\\Leftrightarrow & -891x+495x& = & 77+108 \\\Leftrightarrow & \color{red}{-396} x& = & 185 \\\Leftrightarrow & x = \frac{185}{-396} & & \\\Leftrightarrow & x = \frac{-185}{396} & & \\ & V = \left\{ \frac{-185}{396} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{5})& = & -7x+\frac{7}{3} \\\Leftrightarrow & 24x+\frac{12}{5}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{360}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 360x \color{red}{+36} & = & \color{red}{-105x} +35 \\\Leftrightarrow & 360x \color{red}{+36} \color{blue}{-36} \color{blue}{+105x} & = & \color{red}{-105x} +35 \color{blue}{+105x} \color{blue}{-36} \\\Leftrightarrow & 360x+105x& = & 35-36 \\\Leftrightarrow & \color{red}{465} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{465} & & \\ & V = \left\{ \frac{-1}{465} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{5})& = & 2x+\frac{10}{7} \\\Leftrightarrow & 15x+\frac{6}{5}& = & 2x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{70}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{+42} & = & \color{red}{70x} +50 \\\Leftrightarrow & 525x \color{red}{+42} \color{blue}{-42} \color{blue}{-70x} & = & \color{red}{70x} +50 \color{blue}{-70x} \color{blue}{-42} \\\Leftrightarrow & 525x-70x& = & 50-42 \\\Leftrightarrow & \color{red}{455} x& = & 8 \\\Leftrightarrow & x = \frac{8}{455} & & \\ & V = \left\{ \frac{8}{455} \right\} & \\\end{align}\)