Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{4}{7})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 20x+\frac{20}{7}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{280}{ \color{blue}{14} }x+ \frac{40}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 280x \color{red}{+40} & = & \color{red}{98x} +35 \\\Leftrightarrow & 280x \color{red}{+40} \color{blue}{-40} \color{blue}{-98x} & = & \color{red}{98x} +35 \color{blue}{-98x} \color{blue}{-40} \\\Leftrightarrow & 280x-98x& = & 35-40 \\\Leftrightarrow & \color{red}{182} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{182} & & \\ & V = \left\{ \frac{-5}{182} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{5})& = & -7x+\frac{7}{2} \\\Leftrightarrow & -10x+\frac{8}{5}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-100}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -100x \color{red}{+16} & = & \color{red}{-70x} +35 \\\Leftrightarrow & -100x \color{red}{+16} \color{blue}{-16} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{-16} \\\Leftrightarrow & -100x+70x& = & 35-16 \\\Leftrightarrow & \color{red}{-30} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-30} & & \\\Leftrightarrow & x = \frac{-19}{30} & & \\ & V = \left\{ \frac{-19}{30} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{5}{7})& = & -7x+\frac{5}{12} \\\Leftrightarrow & -6x-\frac{10}{7}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-504}{ \color{blue}{84} }x- \frac{120}{ \color{blue}{84} })& = & (\frac{-588}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -504x \color{red}{-120} & = & \color{red}{-588x} +35 \\\Leftrightarrow & -504x \color{red}{-120} \color{blue}{+120} \color{blue}{+588x} & = & \color{red}{-588x} +35 \color{blue}{+588x} \color{blue}{+120} \\\Leftrightarrow & -504x+588x& = & 35+120 \\\Leftrightarrow & \color{red}{84} x& = & 155 \\\Leftrightarrow & x = \frac{155}{84} & & \\ & V = \left\{ \frac{155}{84} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{4})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -10x+\frac{15}{4}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-280}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{36}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -280x \color{red}{+105} & = & \color{red}{196x} +36 \\\Leftrightarrow & -280x \color{red}{+105} \color{blue}{-105} \color{blue}{-196x} & = & \color{red}{196x} +36 \color{blue}{-196x} \color{blue}{-105} \\\Leftrightarrow & -280x-196x& = & 36-105 \\\Leftrightarrow & \color{red}{-476} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{-476} & & \\\Leftrightarrow & x = \frac{69}{476} & & \\ & V = \left\{ \frac{69}{476} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{7})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 6x+\frac{10}{7}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{42}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 42x \color{red}{+10} & = & \color{red}{35x} +9 \\\Leftrightarrow & 42x \color{red}{+10} \color{blue}{-10} \color{blue}{-35x} & = & \color{red}{35x} +9 \color{blue}{-35x} \color{blue}{-10} \\\Leftrightarrow & 42x-35x& = & 9-10 \\\Leftrightarrow & \color{red}{7} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{4}{5})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -30x-\frac{24}{5}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{-168} & = & \color{red}{245x} +40 \\\Leftrightarrow & -1050x \color{red}{-168} \color{blue}{+168} \color{blue}{-245x} & = & \color{red}{245x} +40 \color{blue}{-245x} \color{blue}{+168} \\\Leftrightarrow & -1050x-245x& = & 40+168 \\\Leftrightarrow & \color{red}{-1295} x& = & 208 \\\Leftrightarrow & x = \frac{208}{-1295} & & \\\Leftrightarrow & x = \frac{-208}{1295} & & \\ & V = \left\{ \frac{-208}{1295} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{5})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -24x-\frac{24}{5}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{-264} & = & \color{red}{385x} +25 \\\Leftrightarrow & -1320x \color{red}{-264} \color{blue}{+264} \color{blue}{-385x} & = & \color{red}{385x} +25 \color{blue}{-385x} \color{blue}{+264} \\\Leftrightarrow & -1320x-385x& = & 25+264 \\\Leftrightarrow & \color{red}{-1705} x& = & 289 \\\Leftrightarrow & x = \frac{289}{-1705} & & \\\Leftrightarrow & x = \frac{-289}{1705} & & \\ & V = \left\{ \frac{-289}{1705} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{5})& = & -7x+\frac{3}{7} \\\Leftrightarrow & 18x+\frac{24}{5}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{+168} & = & \color{red}{-245x} +15 \\\Leftrightarrow & 630x \color{red}{+168} \color{blue}{-168} \color{blue}{+245x} & = & \color{red}{-245x} +15 \color{blue}{+245x} \color{blue}{-168} \\\Leftrightarrow & 630x+245x& = & 15-168 \\\Leftrightarrow & \color{red}{875} x& = & -153 \\\Leftrightarrow & x = \frac{-153}{875} & & \\ & V = \left\{ \frac{-153}{875} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{11})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 12x+\frac{18}{11}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{+18} & = & \color{red}{-55x} +6 \\\Leftrightarrow & 132x \color{red}{+18} \color{blue}{-18} \color{blue}{+55x} & = & \color{red}{-55x} +6 \color{blue}{+55x} \color{blue}{-18} \\\Leftrightarrow & 132x+55x& = & 6-18 \\\Leftrightarrow & \color{red}{187} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{187} & & \\ & V = \left\{ \frac{-12}{187} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{11})& = & 7x+\frac{7}{10} \\\Leftrightarrow & -10x+\frac{8}{11}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1100}{ \color{blue}{110} }x+ \frac{80}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1100x \color{red}{+80} & = & \color{red}{770x} +77 \\\Leftrightarrow & -1100x \color{red}{+80} \color{blue}{-80} \color{blue}{-770x} & = & \color{red}{770x} +77 \color{blue}{-770x} \color{blue}{-80} \\\Leftrightarrow & -1100x-770x& = & 77-80 \\\Leftrightarrow & \color{red}{-1870} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-1870} & & \\\Leftrightarrow & x = \frac{3}{1870} & & \\ & V = \left\{ \frac{3}{1870} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -9x-\frac{12}{5}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{-48} & = & \color{red}{140x} +45 \\\Leftrightarrow & -180x \color{red}{-48} \color{blue}{+48} \color{blue}{-140x} & = & \color{red}{140x} +45 \color{blue}{-140x} \color{blue}{+48} \\\Leftrightarrow & -180x-140x& = & 45+48 \\\Leftrightarrow & \color{red}{-320} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-320} & & \\\Leftrightarrow & x = \frac{-93}{320} & & \\ & V = \left\{ \frac{-93}{320} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{5}{8})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -9x+\frac{15}{8}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-360}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -360x \color{red}{+75} & = & \color{red}{280x} +48 \\\Leftrightarrow & -360x \color{red}{+75} \color{blue}{-75} \color{blue}{-280x} & = & \color{red}{280x} +48 \color{blue}{-280x} \color{blue}{-75} \\\Leftrightarrow & -360x-280x& = & 48-75 \\\Leftrightarrow & \color{red}{-640} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-640} & & \\\Leftrightarrow & x = \frac{27}{640} & & \\ & V = \left\{ \frac{27}{640} \right\} & \\\end{align}\)